Find the matrix A of the reflection in the line L in R2 that consists of all scalar multiples of the vector.

Answer:

hello your question is incomplete attached below is the complete question

answer : 2/13    6/13

               6/13    3/13

Step-by-step explanation:

Firstly we will calculate the orthogonal basis L in R^2

attached below is the detailed solution

also assuming β to be the standard ordered basis

hence the matrix A of the reflection in the Line L in R2 =

2/13    6/13

6/13    3/13

The matrix A of the reflection in line L is given by  [tex]\rm A = \begin{bmatrix}\dfrac{2}{13} & \dfrac{6}{13}\\ \dfrac{6}{13} & \dfrac{3}{13}\end{bmatrix}[/tex]  and this can be determined by first evaluating the value of [tex]\rm R^2[/tex] by using the given data.

The orthogonal basis L in [tex]\rm R^2[/tex] is given by:

[tex]r = [u_1,u_2] =\left[\dfrac{1}{\sqrt{39} }\binom{6}{3}, \dfrac{1}{\sqrt{39} }\binom{3}{-6}\right][/tex]

[tex]\rm T(u_1)=u_1[/tex]

[tex]\rm T(u_2)=0[/tex]

[tex]\rm [T]_r = \begin{bmatrix}1 & 0\\ 0 & 0\end{bmatrix}[/tex]

[tex]\rm Q = \dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}[/tex]

Now, matrix A is given by the formula:

[tex]\rm A=Q[T]_rQ^{-1}[/tex]

Now, substitute the value of known terms in the above equation.

[tex]\rm A = \dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}\begin{bmatrix}1 & 0\\ 0 & 0\end{bmatrix}\dfrac{1}{\sqrt{39} }\begin{bmatrix}6 & 3\\ 3 & -6\end{bmatrix}[/tex]

Simplify the above expression.

[tex]\rm A = \dfrac{1}{{39} }\begin{bmatrix}6 & 18\\ 18 & 9\end{bmatrix}[/tex]

[tex]\rm A = \dfrac{3}{{39} }\begin{bmatrix}2 & 6\\ 6 & 3\end{bmatrix}[/tex]

[tex]\rm A = \dfrac{1}{{13} }\begin{bmatrix}2 & 6\\ 6 & 3\end{bmatrix}[/tex]

Multiply by 1/13 in the matrix.

[tex]\rm A = \begin{bmatrix}\dfrac{2}{13} & \dfrac{6}{13}\\ \dfrac{6}{13} & \dfrac{3}{13}\end{bmatrix}[/tex]

For more information, refer to the link given below:

https://brainly.com/question/16850761

9 correct : 15 questions = 45 correct: q questions
please help me ​

What fraction of state legislatures must approve an amendment before it becomes law​

What is the value of x?

Perform the indicated operation:
NEED HELP PLEASE

There are 7 socks in a bag. 2 of those socks are blue.
What is the probability of picking a blue sock randomly from the bag

Use the Distributive Property to write without parentheses:
4\left(3-2m\right)4(3−2m)

Can anyone solve this? If so tell me and make sure u know what ur doing please

You buy 2,000 shares of stock for $25.43 and sell them for $44.10 per share. What
percent is your capital gain?

NEED HELP SOLVING PLEASE

x divided by 39 = 1204 R38

Find the slope of the line graphed below.

A florist has ordered 632 roses for Valentine's Day. If the roses are divided into 50 bouquets, how many roses will each bouquet
have, and how many roses will be left over?

PLS HELP WILL GIVE BRAINLIEST
How can parents that dont have a O blood type still have a O blood type baby???

What is the original price of the box of cereal?

In the figure,ABC~ DEF. solve for x

The students at Roosevelt Middle School wear uniforms. They may choose to wear either a navy blue or
white shirt each day. Yesterday, 100 of the 150 eighth-grade students wore blue shirts. What was the ratio of
students wearing blue shirts to students wearing white shirts?

if Ladarius jogs 24 km in 3 hours, how many km can he jog in 5 hours?

What is the population density of 13 lillies living in an area of 6 meters (length) and 4 meters (width)?

what is the slope of the line shown?

solve for x.

x/2.5<10​

Pleas help me fast!

Find the zeros for each function
1. f(x)= x^3 + 12x^2 + 21x + 10

2. f(x) = x^4 + x^3 - 11x^2 - 9x + 18

Select all the expressions that are equal to 420.
(40 x 1) + (2 x 10)
30 x 10 x 4
20 x 20 x 1
21 x 20
30 x 14

A line has slope −1. It passes through the point Q(2, −n) and R(4, −3). What is the value of n?

Answer both questions pls for more points :)

Select the correct answer. If the graphs of the linear equations in a system are parallel, what does that mean about the possible solution(s) of the system?
OA The lines in a system cannot be parallel.
OB There is no solution. OC There is exactly one solution.
OD There are infinitely many solutions.​

HELP! WILL GIVE BRANLIEST!
(Question 12)

16. What is the length of minor arc CD?
42
A
d = 30 ft
A: 7.91 feet
B: 8.32 feet
C: 10.99 feet
D: 11.89 feet

8-4x for x = 9
The expression equals I

ashley's tricycle has two different wheel sizes: one larger wheel and two smaller wheels. As Ashley travels the distance between her house and her neighbor's house on the tricycle, the larger wheel rotates 4 times, and each of the small wheels rotate 12 times. If half the circumference of the larger wheel is 2 inches more than the circumference of one of the smaller wheels, what is the distance, in inches, traveled by the tricycle between ashley's house and her neighbor’s house?

A. 4 inches
b. 48
c. 60
d. 16