A denotes an mn matrix. Determine whether the statement is true or false. Justify your answer. The row space of AT is the same as the column space of A.
Answer: true
Step-by-step explanation:
For an m*n matrix, the column space of A will be a space formed by the lineal combination of all the columns of A.
column space = a1*c1 + a2*c2 + ...
where a1, a2, ... are scalars, and c1 is the vector of column 1.
Then we should write:
Column space = a1*(A₁₁, A₂₁, A₃₁, ...) + a2*(A₁₂, A₂₂, A₃₂, ...) + ...
Now, the transpose is defined as:
[At]₁₃ = A₃₁
Here i used the element with subindex 3 and 1, but is the same for every subindex.
Notice that if A is m*n, then [At] is n*m
Now, the row space of [At] will be, same as before.
Row space = b1*r1 + b2*r2 + ...
Where b1, b2, ... are scalars and the r's are the vector of each row.
= b1*( [At]₁₁ , [At]₁₂, [At]₁₃, ...) + b2*([At]₂₁, [At]₂₂, [At]₂₃, ...) + ...
Now we replace each term of the transpose by the associated element in the original matrix.
= b1*( A₁₁, A₂₁, A₃₁, ...) + b2*(A₂₁, A₂₂, ...) + ....
If we take:
b1 = a1, b2 = a2, b3 = a3, ...
We will have that the row space of [At] is the same as the column space of A.
E
Learning Task 2. Give the reciprocal of the given fractions below.
Write your answer in your notebook.
6
1.
6.
2
8.
7
2. 7
7.
1
2
8
3.
8.
4
4
33-
5
als -|- ||-|-
5
4. 41
9.
5
6
5.
1
10. 1
54
5
5
A
Reciprocals represent two numbers whose product is one. Multi-6/8
The correct format of the options are
(1) 6/8 (6) 2/7
(2) 7/2 (7) 1/8
(3) 33[tex]\frac{4}{5}[/tex] (8) 4/5
(4) 41 (9) 5/6
(5) 54[tex]\frac{1}{5}[/tex] (10) 1/5
Answer:
Reciprocal are those number which when multiplied by the original number gives 1 as the result. eg [tex]\frac{6}{8}[/tex] reciprocal is [tex]\frac{8}{6}[/tex], on multiplication [tex]\frac{6}{8}[/tex]*[tex]\frac{8}{6}[/tex] =1
Reciprocal of the following are as follows
(1) [tex]\frac{8}{6}[/tex]
(2) [tex]\frac{2}{7}[/tex]
(3) 33[tex]\frac{4}{5}[/tex] =[tex]\frac{ 33*5 + 4}{5}[/tex] = 169/5 => reciprocal = 5/169
(4) 1/41
(5) 54[tex]\frac{1}{5}[/tex] => [tex]\frac{54*5 +1}{5}[/tex] = 271/5 => 5/271
(6) 7/2
(7) 8
(8) 5/4
(9) 6/5
(10) 5
If the simple interest on $3000 for 3 years is $720 , then what is the interest rate?
Answer:
8%
Step-by-step explanation:
Starting Principal: $
3,000.00
Years:
3
Annual Interest Rate:
8
%
Results
Future Value, using...
Simple Interest: $
3,720.00
Annually Compounded Interest: $
3,779.14
I WILL MARK BRAINLIST
Question 9
Answer:
True
Step-by-step explanation:
Marcus likes Nike sneakers. He paid $195 for a sneaker that originally cost $245. What is the percent discount of his purchase?
Answer:
21%
Step-by-step explanation:
195 divided by 245 = 0.79 approximately
100-79=21
Always divide the small number by the big number for percentages
Good luck!
Find the measure of angle b.
4)
36°
what do you guys think
Which expression is equivalent to y^3-2y^2+y
Answer:
the first one i did it yesterday
The chart below contains the results of a survey in which students were asked about their cell phone plan.
Cell Phones Plans
Plan
Students
No cell phone
20
Voice only
14
Voice and texting
12
Voice, texting, and data
4
What percent of the students surveyed have a phone plan with texting?
16%
24%
32%
68%
If you get it right you get the crown brain thing
Answer:
It is option C.
Step-by-step explanation:
I did the test.
Answer:
it c
Step-by-step explanation:
i did the unit test hope this helps :)
find the original price of a pair of shoes if the sale price is $40 after a 60% discount
Answer:
Thus, the original price of the pair of shoes was $100.
Step-by-step explanation:
Percentages
After a 60% discount, the sale price is now valued at 100-60=40% of its original price.
If the sale price is $40, then the original price is calculated as
$40 / 40 * 100 = $100
Thus, the original price of the pair of shoes was $100.
Verify applying 60% discount:
$100 - 60*$100/100 = $40
GIVING BRAINLIEST IF CORRECT PLEASE HELP ASA[P
Answer:
Step-by-step explanation:
1: Green because it has more sections than the other colors
2: 4/8
Hope this helps!
Answer:
A) green
B) 4/8
brainliest please
What is the solution to this equation?
3x-9 = 12
O A. x = 1
B. x = 7
O c. x = 9
O D. x = 63
There are 3,785 milliliters in 1 gallon, and there are 4 quarts in 1 gallon.
How many milliliters are in 3 gallons?
Answer:11,356
Step-by-step explanation: that is the answer! I’m sure
Answer:11.355
Step-by-step explanation:
A 6-kilogram bag of cat food costs $21.54. What is the unit price?
Answer:0.27855153
A
−
0.04642525
kilograms per dollar
Step-by-step explanation:
8.
Andrew has $76.50. Elijah has $94.30. How much more money does Elijah have than
Andrew
Answer:
$17.80Step-by-step explanation:
This is a fairly simple question. All we need to do is find the difference between the two amounts.
$94.30 - $76.50 = $17.80
A new hard drive costs $225, plus $40 per hour for labor. The linear equation y = 40x + 225 gives the cost y in dollars for x hours of labor. If Jane has $385 to spend on computer repairs, using plug and chug strategy for x hours of labor, what is the maximum number of hours the computer technician can work?
Answer:
Step-by-step explanation:
225+40h=y
225 + 40x = 385
-225 -225
------- -------
40x = 160
x= 4
a family rents a cottage for $79.95 a day for 7 days. about how much does the family pay for the cottage?
Answer:
$560
Step-by-step explanation:
Since the family rents a cottage for 7 days, 79.95 dollars each day, we multiply 79.95 by 7 and get 559.65. Since the question asks about how much does the family pay, we round 559.65 to get $560.
p – 22 < 40 . could you give me the answer and the steps thank you!
Answer:
the answer is 62
Step-by-step explanation:
ok so all you do is add 22 instead of subtracting 22
1) The membership fee of Math Club is P25. What is the total amount
paid by 1,252 members?
A. P 31,250
B. P 31,252
C. P 31,230
Answer:
it's actually none of those the answer I have is p 31,300
IF UR GOOD AT PRECALC PLEASE HELP
Answer:
Answer is C, u can find this just by looking at domain
How do break down what is the percentage of change in cost of the pizza
It’s it A B C D please answer
Answer:
It is B. I hope this helps.
Step-by-step explanation:
Find the solutions to the equation below.
Check all that apply.
6x2 + 7x -5 = 0
A. x = 1/3
B. x = 5
c. x = -5/3
D. x = -1/3
E. x = 1/2
F. x = -2
Answer:
A and C
Step-by-step explanation:
Move all terms to the left side and set equal to zero. Then set each factor equal to zero
what is 2+2 my brain has been in circles about this
Answer:
hey welcome to Brainly, and 2 + 2 = 4
Step-by-step explanation:
2+2=4
3+3=6
4+4=8
5+5=10
and so on just keep adding 2
Help
Brainliest in reward
Please name both angles
Which two numbers below have a least common multiple of 48?
Answer:
its 3 and 16 just trust me
The least common multiple is divisible by both a and b. The two numbers below have a least common multiple of 48 is 3 and 16.
What is LCM?The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.
The two numbers below have a least common multiple of 48 are,
3 and 16 ⇒ 3×16=48
Hence, the two numbers below have a least common multiple of 48 is 3 and 16.
Learn more about LCM:
https://brainly.com/question/20739723
#SPJ2
Two forces are acting on an object, one at 58 Newton's and the other at 83 Newton's.
The resulting force is 105 Newton's. What is the angle between the resulting force and
the larger of the two original forces?
Does anyone understand this?
Answer:
no looks confusing
Step-by-step explanation:
Select each situation that can represent a proportional relationship
The price of buying x gallons of gas at $3 a gallon.
The total amount of weight a kitten gains in w weeks when it gains 4 ounces per week and started at a weight of 6 ounces.
The price of renting a scooter for m miles when it costs $0.75 per mile plus a base fee of $2.50.
The total amount of money a child earns from doing chores when she earns $10 a week for w weeks.
Plz help!
Answer:
The 1st one and the last one
Step-by-step explanation:
point A is located in which quadrant 1 2 3 or 4
Answer:
I THINK 2
Step-by-step explanation:
Answer: (-3, 5) : Quadrant 2
The expression factors as: (n4 + 3)(n4 + 3)
(n4 - 3)(n4 + 3)
(n4 – 3)(n4 – 3)
Answer:
(n 4)
Step-by-step explanation:
Answer:
B - the second one (on EDGE)
Step-by-step :
