c=1/2 which makes fx|y (x, y) a valid conditional probability mass function.
What is conditional probability?
The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is determined by multiplying the likelihood of the earlier event by the increased likelihood of the later, or conditional, event.
Given that;
p(x) = [tex]c (\frac{2}{3} )^n[/tex] where x = 1,2,3,........
for getting value of c we are using the expression :
[tex]\sum_{n=1}^{\infty} c(\frac{2}{3})^n = 1[/tex]
[tex]c\sum_{n=1}^{\infty} (\frac{2}{3})^n = 1[/tex]
Since we want p(x) to be a Probability Mass Function, your approach is correct, since for any such function
fX:A→[0,1],X:S→A⊆R, it is :
[tex]\sum _{x\in A} \ fX(x)=1[/tex]
As long as you've correctly understood that condition, you can proceed with your specific exercise as follows:
[tex]\sum_{n=1}^{\infty} c(\frac{2}{3})^n = 1[/tex]
⇔ [tex]c\sum_{n=1}^{\infty} (\frac{2}{3})^n = 1[/tex]
⇔2c = 1
⇔c = 1/2
Hence c = 1/2 is the valid conditional probability mass function.
Learn more about conditional probability click here:
https://brainly.com/question/10739997
#SPJ4
simplify (8^(5))/(8^(-9))
1.8^-45
2.8^-4
3.8^14
4.8^45
The expression (8^(5))/(8^(-9)) is simplified to 8^14. Option 3
What are index forms?Index form of a number can simply be described as that number written in the form of an exponential expression.
The number can also be written as a single number which is raised to another number.
Some rules of indices to note;
Multiplying index form results in addition of their powersDivision results in subtraction of their powersGiven that;
(8^(5))/(8^(-9))
Then, we have;
8^5-(-9)
8^5+9
Add the powers
8^14
Hence, the value is 8^14
Learn more about index forms here:
https://brainly.com/question/15361818
#SPJ1
Student are going on a field trip to a play. The play i elling kid ticket and adult ticket. They old a total of 60 ticket. One kid ticket ell for $3 while the adult ticket i $5. They made a profit of $220 that day. How many kid ticket were old?
Number of kids ticket is 40
What do you mean by system of linear equation?
A set of two linear equations with two variables is a system of linear equations. There are infinitely many possible solutions to a linear equation with two variables. There can be a single solution to a system of two linear equations with two variables that satisfies both solutions. It is necessary to combine two equations with two variables into one equation with one variable while solving a system of equations.
Total number of tickets = 60
Cost of 1 kid ticket = $3
Cost of 1 adult ticket = $5
Total profit = $220
Let number of kid tickets = x
number of adult tickets = y
According to question:
x + y = 60 ......(1)
3x + 5y = 220 ........(2)
Substitute the value of x from eq(1) to eq(2)
3(60 - y) + 5y = 220
180 - 3y + 5y = 220
180 + 2y = 220
2y = 220 - 180
2y = 40
y = 40/2
y = 20
Substitute this value of y in eq(1)
x + 20 = 60
x = 60 - 20
x = 40
Therefore, number of kids ticket is 40
To learn more about linear equation from the given link.
https://brainly.com/question/2030026
#SPJ4
what is the equation in slope intercept form of the line that passes through the point (-0.5,7) and is parallel to the graph of y=-8x-2 please help
Answer:
y = -8x + 3
Step-by-step explanation:
Pre-SolvingWe are given that a line passes through the point (-0.5,7), and is parallel to y = -8x - 2
We want to write the equation of this line in slope-intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept, hence the name.
Parallel lines have the same slopes.
Therefore, we can start by finding the slope of y = -8x - 2.
It is also written in slope-intercept form. -8 is where m (slope) should be; therefore, the slope of the line is -8.
SolvingWe can plug in -8 for m in y=mx+b.
y = -8x + b
Now we need to find b.
As the equation passes through the point (-0.5,7), we can use its values to help solve for b.
Substitute -0.5 as x and 7 as y.
7 = -8(-0.5) + b
Multiply
7 = 4 + b
Subtract 4 from both sides
3 = b
Substitute 3 as b in the equation.
y = -8x + 3
Topic: parallel and perpendicular lines
See more: https://brainly.com/question/26202010
a penny is thrown from the top of a 52.6-meter building and hits the ground 3.31 seconds after it was thrown. the penny reached its maximum height above the ground 0.85 seconds after it was thrown. define a quadratic function, h , that expresses the height of the penny above the ground (measured in meters) as a function of the number of seconds elapsed since the penny was thrown, t.
The quadratic function which models the motion of the penny is
h(t) = -4.9t² -0.327761 t + 52.6
and the maximum height reached is 57.43
h(t) = - 0.5gt² + vt + h
g = 9.8 m/s²
h = 52.6 m
v = ?
For v,
h(t) = -0.5gt² + vt + 52.6
h(t) = - 4.9t² + vt + 52.6
Time when penny hits the ground ; t = 3.31
h(3.31) = 0
0 = -4.9(3.31)² + v(3.31) + 52.6
0 = -53.68489 + 3.31v +52.6
3.31v = -1.08489
v = -1.08489/3.31
v = -0.327761 m/s
Therefore,
h(t) = -4.9t² -0.327761 t + 52.6
2.) Maximum height of the penny above the ground
t = 0.85 seconds
h(0.85) = -4.9(0.85^2)-0.327761 (0.85) + 52.6
Maximum height reached = 57.43 meters
Therefore, the maximum height reached is 57.43 meters.
An object changing its position with regard to time is referred to as motion. Motion is mathematically characterised in terms of displacement, distance, velocity, acceleration, and speed as well as the observer's frame of reference and the measurement of the change in the body's position with respect to that frame over time. Kinematics is the area of physics that studies how motion is affected by forces, whereas dynamics is the area that studies how motion is affected by forces.
To learn more about motions
https://brainly.com/question/18980389
#SPJ4
The bill for two book came to $28. 48. One book cot $7. 44. What wa the cot of the other one
Answer:
Step-by-step explanation:
Ok:
If the two books together costs $28.48 and one of them cost $7.44 Subtract to get the other book's price
2. 28.45-7.44=$21.01
3. Answer: The cost of the other one is $21.01
please help im suffering right now
Answer:
C
Step-by-step explanation:
If we use the distributive property for 4 (2x + 1), we see that 4 (2x) = 8x and that 4 (1) = 1. That means 4 (2x + 1) = 8x + 4 which is not equivalent to 2x + 4y. So this limits our answer to either C or D. C is the correct answer because if we use the distributive property again here for 4 (2x + y), we see that 4 (2x) = 8x and 4 (y) = 4y. That means that 4 (2x + y) = 8x + 4y which is the answer we're looking for.
May I please have brainliest for this? Thank you very much!
A mountain climber found that the relationship between his altitude and the surrounding air temperature is linear. The function
represents this relationship, where is the altitude in meters and is the temperature in degrees Fahrenheit. According to this function, by how much is the temperature decreasing for every meter that the mountain climber’s altitude increases?
The temperature decrease for every meter that the mountain climber's altitude increases is given by:
-100 ºF.
What is the temperature decrease?The function that models this situation is a linear function, which has the format defined as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope of the function, representing by how much y changes when x is increased by one.b is the y-intercept of the function, representing the numeric value of y when x = 0.In the context of this problem, the function is defined as follows:
f(a) = -100a + 75.
Hence the slope of the function is of:
-100.
Representing the temperature decrease for each meter of altitude increase of the climber.
Missing InformationThe function is defined as:
f(a) = -100a + 75.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
The table shows the ingredients for one batch of barbecue sauce. Anne has 9 cups of ketchup and makes the greatest number of whole batches of barbecue sauce possible. How much ketchup remains?
Answer:
hi do you mind making the question a bit clear? where is the table?
Step-by-step explanation:
pls help right now I need help
giving brainliest
this is reading btw
Answer:
The answer is A
Step-by-step explanation: I'm so smart
I need help please im so confused
Step-by-step explanation:
the x-intercept is the point, where the curve intercepts the x-axis (that means y = 0).
the y-intercept is the point, where the curve intercepts the y-axis (that means x = 0).
y = 10 - 2x
when x = 0, that means y = 10 - 2×0 = 10.
when y = 0, that means 0 = 10 - 2x, 2x = 10, x = 5
x-intercept = (5, 0)
y-intercept = (0, 10)
4y + 9x = 18
x = 0, 4y = 18, y = 18/4 = 9/2 = 4.5
y = 0, 9x = 18, x = 18/9 = 2
x-intercept = (2, 0)
y-intercept = (0, 4.5)
6x - 2y = 44
3x - y = 22
x = 0, -y = 22, y = -22
y = 0, 3x = 22, x = 22/3 = 7 1/3
x-intercept = ( 7 1/3, 0)
y-intercept = (0, -22)
2x = 4 + 12y
x = 2 + 6y
x = 0, 6y = -2, y = -2/6 = -1/3
y = 0, x = 2 + 6×0 = 2
x-intercept = (2, 0)
y-intercept = (0, -1/3)
Which equation represents the partial sum of the geometric series? 125 + 25 + 5 + 1.
The correct option which represents sum expressed in sigma notation is A.
What is sigma notation?
A series is represented in an exceedingly compact type, referred to as summation or sigma notation. The greek capital letter, ∑ , is employed to represent the total.
The series 4+8+12+16+20+24 is expressed as ∑n= 4n . The expression is browse because the total of 4n as n goes from one to six . The variable n is termed the index of summation.
The geometric series.
Main body:
∑ 125 (1/5)ⁿ⁻¹ ; where, n = 1 to 4.
Now, Calculate the partial sum of the geometric series as;
The geometric series = ∑ 125 (1/5)ⁿ⁻¹
Substitute n = 1, 2, 3, 4, we get;
= 125 (1/5)¹⁻¹ + 125 (1/5)²⁻¹ + 125 (1/5)³⁻¹ + 125 (1/5)⁴⁻¹
= 125 (1/5)⁰ + 125 (1/5)¹ + 125 (1/5)² + 125 (1/5)³
= 125 + 25 + 125/25 + 125/125
= 125 + 25 + 5 + 1
Thus, The partial sum of the geometric series is;
⇒ 125 + 25 + 5 + 1
Option A is true.
The correct question is in the figure.
To know more about sigma notation ,, visit:
brainly.com/question/26243301
#SPJ4
If the lowest price in the past year occurred 35 days ago, find the approximate average change per day since then. a. $2.08 b. $2.64 c. $0.90 d. $2.99
The approximate change per day since the lowest price occurred 35 days ago, is a. $2.08.
How to find the approximate average change?The approximate average change can be found by the formula :
= ( Current price of stock - Lowest price ) / Number of days since lowest price
Current price of Dagofi Radar stock = $ 130. 58 closing price
Lowest price = $ 57. 71
The approximate average change is:
= ( 130. 58 - 57. 71) / 35
= 72. 87 / 35
= $ 2.08
Find out more on approximate average change at https://brainly.com/question/22409149
#SPJ1
Missing part of question:
Consider today's stock listing for Dagofi Radar, shown below.
52 wk High
52 wk Low
Symbol
Div.
Close
Net Change
162.22
57.71
DFR
9.75
130.58
-2.64
recursively define the set of binary strings with more 0s than 1s.
0>1,If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y.
What do binary strings mean?A series of bytes make up a binary string. A binary string is used to store non-traditional data, including images, as opposed to a character string, which typically holds text data. The quantity of bytes in a binary string determines its length. The CCSID for a binary string is 65535.Binary refers to this system of 1s and 0s. Because of the way they are made, computers only speak in binary. A computer is nothing more than a sizable number of switches. On those curiously engraved boards inside the computer, there are millions of microscopic electronic switches.If a function f is constructed recursively, at least one of its values, f(x), must be defined in terms of f(y), where x>y. A procedure P is defined recursively if its action, P(x), is defined in terms of another action, P(y), where x>y.Explanation:
0>1.
To learn more about Binary string refer to:
https://brainly.com/question/29739112
#SPJ4
Given f(x)=3x+4f(x)=3x+4, find f(4)f(4).
Answer:
f(x) = 3x + 4
f(4) = 3(4) + 4 = 12 + 4 = 16
A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If
x machines are made, then the unit cost is given by the function C(x)=1.2²-600x+82,738. What is the minimum unit cost?
Do not round your answer.
The minimum unit cost is 7738 when the function is C(x)=1.2x²-600x+82,738
What is meant by unit cost?A company's unit cost is the cost of producing, storing, and selling one unit of a specific product. Unit costs encompass all fixed and variable production costs. A cost unit is a quantity measuring unit for a product or service.
A unit cost is the overall cost incurred by a business to manufacture, store, and sell one unit of a specific product or service. Unit costs are the same as cost of goods sold (COGS). This accounting metric incorporates all fixed and variable expenses related with the manufacture of a good or service.
Given,
C(x)=1.2x²-600x+82,738
Minimum value [tex]C_{min}[/tex]=c-(b²/4a)
Where a=1.2, b=-600, c=82738
[tex]C(x)_{min}[/tex]=82738-((-600)²/4(1.2))
=82738-(360000/4.8)
=7738
Therefore, the minimum unit cost is 7738.
Hence, the minimum unit cost is 7738 when the function is C(x)=1.2x²-600x+82,738
To know more about variable cost, visit:
https://brainly.com/question/15358722
#SPJ1
Michael swam 2,000 yards on each of eighteen days.
The scatterplot above shows his swim time for and
corresponding heart rate after each swim. The line of
best fit for the data is also shown. For the swim that
took 34 minutes, Michael's actual heart rate was
about how many beats per minutes less than the rate
predicted by the line of best fit?
A) 1
B) 2
C) 3
D) 4
Michael's actual heart rate was about 2 beats per minutes less than the rate predicted by the line of best fit. The correct option is B
What is a scatterplot?A scatterplot is a data visualization that depicts the relationship between two numerical variables. Each dataset member is plotted as a point whose x-y coordinates correspond to its values for the two variables.
On each of the eighteen days, Michael swam 2,000 yards. The scatterplot above depicts his swim time and heart rate after each swim. The data's best fit line is also shown.
From the graph the actual heart rate=150
but calculated heart rate from best fit line=148
Difference between actual and calculated=150−148=2
Option B is correct.
Learn more about scatterplot on:
https://brainly.com/question/6592115
#SPJ1
. If g = -4 and h = -5 find the value of
a) 4gh
b) g²h
c) 5h - g²
Answer:
a) 80
b) -80
c) -41
Step-by-step explanation:
For g = -4 and h = -5, you want the values of ...
4ghg²h5h -g²To evaluate these expressions, put the value of the variable where the variable is, and do the arithmetic. A calculator can help.
a) 4gh= 4(-4)(-5) = 80
b) g²h= (-4)²(-5) = -80
c) 5h -g²= 5(-5) -(-4)² = -25 -16 = -41
Solve for x:
7x(x+1. 8)=0
Need help ASAP.
Answer is not x=-1. 8 or x=0
Answer:
Step-by-step explanation:
x = -9/5 = -1.800 or
x = 0
ABCD is a rectangle, where AB= x cm and
BC is 1.5 cm less than AB.
If the area of the rectangle is 52 cm³, form
an equation in x and solve it to find the
dimensions of the rectangle.
Answer:
AB = 8cm ; BC = 6.5 cm
Step-by-step explanation:
BC = x- 1.5
x * (x-1.5) = 52
x^2 - 1.5x - 52 = 0
Discriminant = 2.25 -4(-52) = 2.25 + 208 = 210.25
We are searching only positive value
(1.5 + 14.5)/2 = 16 / 2 = 8 cm
AB = 8 cm
BC = 8 - 1.5 = 6.5 cm
7(x-1)=3x+2 in a improper fraction
Answer:x=9/4 nine over 4 for improper fraction I hope this is helpful mark me brainlist if this sounds good
Step-by-step explanation:
7(x-1)=3x+2
Distribute through the parentheses
7x-7=3x+2
Move the variable to the left-hand side and change its sign
7x-7-3x=2
or Move the constant to the right-hand side and change its sign
7x-7-3x=2
Collect like terms
4x=2+7
And then Add the numbers
4x=9
Divide both sides of the equation by 4
x=9/4
Mixed number is 2 1/4
I need help with this question, I don't understand how we get the x value in the equation.
I'm not trying to cheat, I just need steps to see how we get to the end of it.
y=x-1
y=-x+3
Step-by-step explanation:
the x value comes from the slope when graphing. for example, the slope on this problem is just x which means its only one. so you move up one and to the right one. for the second equation, its negative so you move back one or down one. the x value coms from when they are both intercepted when graphed.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeehelp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Step-by-step explanation:
b.) 8/7≈ 1.1
Final.) and then using the exponential decay formula, 18.1 will be left after
prove: if the bisector of an exterior angle of a triangle is parallel to a side of the triangle, the triangle is isosceles
The proof that if bisector of an exterior angle of a triangle is parallel to a side of triangle, triangle is isosceles is shown below .
In the question ,
it is given that ,
the angle bisector of the exterior angle of a triangle is parallel to a side .
we have to prove that the triangle will be an isosceles triangle .
In the triangle ABC given below , AB is extended to AD ,
SO , the exterior angle will be angle DAC ,
let AE be the bisector of the the angle .
So , the equal angles are angle DAC and angle EAC .
it is given that AE is parallel to BC , where BC is base .
we know that ,
if any line intersects two parallel lines then every pairs of alternative Interior angles are same and also their corresponding angles are equal .
Here AE is parallel to BC and line BD intersects them ,
So , angle ABC = angle DAE ( corresponding angles )
angle ACB = angle EAC ( alternate angles )
Now , as AE is the bisector of angle DAC ,
we have , angle DAC = angle EAC
So , we get , angle ABC = angle ACB .
In triangle triangle ABC two angles are equal so , the sides opposite to angles to angles will also be equal
that means , AB=AC
Hence , the given Triangle is an isosceles triangle .
Therefore , it is proved that the triangle ABC is an isosceles triangle .
Learn more about Isosceles Triangle here
https://brainly.com/question/21475560
#SPJ4
Let the random variable b represent the number of books a student buys at the next book fair. What is the expected value of b ?.
The expected value of the random variable b is given as follows:
2.404 books.
How to obtain the expected value of a discrete probability distribution?The expected value of a discrete probability distribution is given by the sum of each outcome of the distribution multiplied by it's respective probability.
From the histogram given by the image at the end of the answer, the distribution is given as follows:
P(X = 1) = 0.285.P(X = 2) = 0.333.P(X = 3) = 0.168.P(X = 4) = 0.136.P(X = 5) = 0.063.P(X = 6) = 0.015.Then the expected value of the random variable b is obtained as follows:
E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 = 2.404 books.
Missing InformationThe histogram is given by the image at the end of the answer.
More can be learned about the expected value of a discrete distribution at https://brainly.com/question/27899440
#SPJ1
Examine the table, which represents the number of guests visiting a museum during a period of time.
If the relationship between hours and guests is proportional, what is the value of h?
Enter your answer as a number, like this: 42
Answer:
7
Step-by-step explanation:
649-531=118
We know that there are 118 more guests per hour.
Divide 826 by 118 to get 7.
Answer: 7
Step-by-step explanation:
The first line of the table is 2 and 236 if you divide 236 by 2 you get 118
Then after that you times it by any number after 5.5 until you get 826.
Which polygon appears to be regular?
Answer:
Figure b
Step-by-step explanation:
the sides are equal
I need help with 9 10 and 11
help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!help meeeeeeeeeeeeeeeeeee pleaseee!!!!
a. [tex]123.1(1.069)^3 \approx 150.4[/tex]
b. [tex]123.1(1.069)^{20} \approx 467.5[/tex]
Select all correct answers. one solution to a quadratic equation is . what is true about any remaining solutions? there are at least two more real solutions. there are no other real solutions. there is exactly one complex solution. there are two or more complex solutions. there are no complex solutions. there is exactly one more real solution.
There is exactly one more real solution or there is exactly one more complex solution
Given,
One solution to a quadratic equation is x = -5/3
We have to find the correct statements from the given ones;
A polynomial of degree two is a quadratic equation.
This implies that a polynomial has two solutions.
We already have an answer to the query, which is a true root.
Then, the additional response that we lack can appear in the form of two responses.
It may be a real root or a complicated root, depending on the situation.
The following is the response to this query:
There is exactly one more real solution or there is exactly one more complex solution
Learn more about quadratic equation here;
https://brainly.com/question/18361805
#SPJ4
33. Let M2x2 be the vector space of all 2x 2 matrices, and define T : M2x2 → Mo by T(A) A + AT, where a. Show that T is a linear transformation. b. Let B be any element of M2 c. Show that the range of T is the set of B in M2x2 with the d. Describe the kemel of T such that BT B. Find an A in M2xz such that T(A) B property that B B
a) T( K₁A₁+K₂A₂)= K₁T(A₁)+K₂T(A₂). So, T is a linear transformation.
b) T(A)=B, if B be any element of M₂
c) Range of T=={A∈ [tex]M_{ 2*2}[/tex]/[tex]A^{T}[/tex]=-A}
What is meant by matrix?A matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions arranged in rows and columns that is used to represent a mathematical object or an attribute of such an item.
A square matrix's determinant is a number connected with the matrix that is crucial for studying a square matrix; for example, a square matrix is invertible if and only if it has a nonzero determinant, and a square matrix's eigenvalues are the roots of a polynomial determinant.
Define T: [tex]M_{ 2*2}[/tex] ⇒ [tex]M_{ 2*2}[/tex] by T(A)=A+[tex]A^{T}[/tex]
a) Let T is a linear transformation
Consider K₁A₁+K₂A₂ ∈ [tex]M_{ 2*2}[/tex]
T( K₁A₁+K₂A₂)= K₁A₁+K₂A₂+( K₁A₁+K₂A₂)[tex]( K₁A₁+K₂A₂)^{T}[/tex]
= K₁T(A₁)+K₂T(A₂)
T( K₁A₁+K₂A₂)= K₁T(A₁)+K₂T(A₂)
Therefore, T is a linear transformation.
b) Let B∈ [tex]M_{ 2*2}[/tex] such that [tex]B^{T}[/tex]=B
Therefore, B is a symmetric matrix.
Let A=(1/2)B∈ [tex]M_{ 2*2}[/tex]
T(A)=A+[tex]A^{T}[/tex]
=(1/2)B+[tex](1/2B)^{T}[/tex]
T(A)=B
A=(1/2)B such that T(A)=B
c) Range of T is the set of B in [tex]M_{ 2*2}[/tex], [tex]B^{T}[/tex]=B
T( [tex]M_{ 2*2}[/tex])={B∈ [tex]M_{ 2*2}[/tex]/ [tex]B^{T}[/tex]=B}
d) Kernel of T={A∈ [tex]M_{ 2*2}[/tex]/T(A)=0)
={A∈ [tex]M_{ 2*2}[/tex]/A+[tex]A^{T}[/tex]=0}
={A∈ [tex]M_{ 2*2}[/tex]/[tex]A^{T}[/tex]=-A}
To know more about matrix, visit:
https://brainly.com/question/28180105
#SPJ1
Three points Assuming M22 is the vector space containing all 22 matrices, T: M22 M22 is defined as T(A) = A + AT.
T is a linear transformation, therefore demonstrate it.
b) Assume that B is any element from M22 where BT = B. In M22, look for an A such that T(A) = B.
c) Explain the T kernel.
a) Verifying that T preserves sums and multiplication by scalars—which implies that T(0) = 0 in particular—is sufficient to determine if T is linear.
Additions: T(A+B) = A+B+A+B T = A+B+A T +B
T = (A + A T ) + (B + B T ) = T(A) + T (B).
Scalar multiplication
T(c · A) = (c · A)
T = c · A
T = c · T(A) (A).
b) Calculate A = 1 2B. Since AT = 1 2BT = 1 2B, T(A) = A + A.
T = \s1 \s2 \sB + \s1 \s2 \sB = B.
c) If 0 0 0 0 = A + A, then and only if A = a b c d, A is in the kernel of T.
If and only if 2a = b + c = 2d = 0, i.e., a = d = 0 and c = b, then T = a b c d + a c b d = 2a b + c b + c 2d. Therefore, the set ker(T) = 0 b b 0 : b R is the kernel of T.
To know more about vector space visit:
https://brainly.com/question/13058822
#SPJ1
