Question

Linear Algebra Find the 2x2 matrix A of a linear transformation T: R^2->R^2 such that T(vi)...

Linear Algebra

Find the 2x2 matrix A of a linear transformation T: R^2->R^2 such that T(vi) = wi for i = 1,2.

v1=(4,3), v2=(5,4); w1=(-3,2), w2=(-3,-4)

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
consider the basis S={v1,v2} for R^2,where v1=(-2,1) and v2=(1,3),and let T:R^2-R^3 be linear transformation such that...
consider the basis S={v1,v2} for R^2,where v1=(-2,1) and v2=(1,3),and let T:R^2-R^3 be linear transformation such that T(v1)=(-1,2,0) And T(v2)=(0,-3,5), find T(2,-3)
Linear algebra Find a transformation matrix A for P^2 -> P^3 then show its onto
Linear algebra Find a transformation matrix A for P^2 -> P^3 then show its onto
1. Find the orthogonal projection of the matrix [[3,2][4,5]] onto the space of diagonal 2x2 matrices...
1. Find the orthogonal projection of the matrix [[3,2][4,5]] onto the space of diagonal 2x2 matrices of the form lambda?I.   [[4.5,0][0,4.5]]  [[5.5,0][0,5.5]]  [[4,0][0,4]]  [[3.5,0][0,3.5]]  [[5,0][0,5]]  [[1.5,0][0,1.5]] 2. Find the orthogonal projection of the matrix [[2,1][2,6]] onto the space of symmetric 2x2 matrices of trace 0.   [[-1,3][3,1]]  [[1.5,1][1,-1.5]]  [[0,4][4,0]]  [[3,3.5][3.5,-3]]  [[0,1.5][1.5,0]]  [[-2,1.5][1.5,2]]  [[0.5,4.5][4.5,-0.5]]  [[-1,6][6,1]]  [[0,3.5][3.5,0]]  [[-1.5,3.5][3.5,1.5]] 3. Find the orthogonal projection of the matrix [[1,5][1,2]] onto the space of anti-symmetric 2x2 matrices.   [[0,-1] [1,0]]  [[0,2] [-2,0]]  [[0,-1.5] [1.5,0]]  [[0,2.5] [-2.5,0]]  [[0,0] [0,0]]  [[0,-0.5] [0.5,0]]  [[0,1] [-1,0]] [[0,1.5] [-1.5,0]]  [[0,-2.5] [2.5,0]]  [[0,0.5] [-0.5,0]] 4. Let p be the orthogonal projection of u=[40,-9,91]T onto the...
Suppose R: |R^2 -> |R^2 is the linear transformation: R( x1 , x2) = (x2 ,...
Suppose R: |R^2 -> |R^2 is the linear transformation: R( x1 , x2) = (x2 , x1) a) Give a geometric description of R. b) Compute the matrix of R relative to te standard basis of |R^2 c) Let v1 = (1, 1) and v2 = (1, -1) Verify that B = (v1, v2) is a basis for |R^2, and compute the matrix of R relative to the basis B, i.e [R]B
Find the standard matrix for the following transformation T : R 4 → R 3 :...
Find the standard matrix for the following transformation T : R 4 → R 3 : T(x1, x2, x3, x4) = (x1 − x2 + x3 − 3x4, x1 − x2 + 2x3 + 4x4, 2x1 − 2x2 + x3 + 5x4) (a) Compute T(~e1), T(~e2), T(~e3), and T(~e4). (b) Find an equation in vector form for the set of vectors ~x ∈ R 4 such that T(~x) = (−1, −4, 1). (c) What is the range of T?
LINEAR ALGEBRA For the matrix B= 1 -4 7 -5 0 1 -4 3 2   ...
LINEAR ALGEBRA For the matrix B= 1 -4 7 -5 0 1 -4 3 2    -6 6    -4 Find all x in R^4 that are mapped into the zero vector by the transformation Bx. Does the vector: 1 0 2 belong to the range of T? If it does, what is the pre-image of this vector?
Problem 2. (20 pts.) show that T is a linear transformation by finding a matrix that...
Problem 2. (20 pts.) show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2, ... are not vectors but are entries in vectors. (a) T(x1, x2, x3, x4) = (0, x1 + x2, x2 + x3, x3 + x4) (b) T(x1, x2, x3, x4) = 2x1 + 3x3 − 4x4 (T : R 4 → R) Problem 3. (20 pts.) Which of the following statements are true about the transformation matrix...
Assume that T is a linear Transformation. a) Find the Standard matrix of T is T:...
Assume that T is a linear Transformation. a) Find the Standard matrix of T is T: R2 -> R3 first rotate point through (pie)/2 radian (counterclock-wise) and then reflects points through the horizontal x-axis b) Use part a to find the image of point (1,1) under the transformation T Please explain as much as possible. This was a past test question that I got no points on. I'm study for the final and am trying to understand past test questions.
Determine whether or not the transformation T is linear. If the transformation is linear, find the...
Determine whether or not the transformation T is linear. If the transformation is linear, find the associated representation matrix (with respect to the standard basis). (a) T ( x , y ) = ( y , x + 2 ) (b) T ( x , y ) = ( x + y , 0 )
Problem 2. Show that T is a linear transformation by finding a matrix that implements the...
Problem 2. Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x1, x2, ... are not vectors but are entries in vectors. (a) T(x1, x2, x3, x4) = (0, x1 + x2, x2 + x3, x3 + x4) (b) T(x1, x2, x3, x4) = 2x1 + 3x3 − 4x4 (T : R4 → R)​ Please show T is a linear transformation for part (a) and (b).
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT