Question

Find the matrix A in the linear transformation y = Ax,where a point x = [x1,x2]^T...

Find the matrix A in the linear transformation y = Ax,where a point x = [x1,x2]^T is projected on the x2 axis.That is,a point x = [x1,x2]^T is projected on to [0,x2]^T . Is A an orthogonal matrix ?I any case,find the eigen values and eigen vectors of A .

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
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).
(12) (after 3.3) (a) Find a linear transformation T : R2 → R2 such that T...
(12) (after 3.3) (a) Find a linear transformation T : R2 → R2 such that T (x) = Ax that reflects a vector (x1, x2) about the x2-axis. (b) Find a linear transformation S : R2 → R2 such that T(x) = Bx that rotates a vector (x1, x2) counterclockwise by 135 degrees. (c) Find a linear transformation (with domain and codomain) that has the effect of first reflecting as in (a) and then rotating as in (b). Give the...
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...
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 )
A linear transformation T : Rn → Rn is an orthogonal transformation if and only if...
A linear transformation T : Rn → Rn is an orthogonal transformation if and only if T(x)⋅T(y) = x ⋅y for all vectors x and y in Rn. True or false?
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?
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.
Consider the transformation T: R2 -> R3 defined by T(x,y) = (x-y,x+y,x+2y) Answer the Following a)Find...
Consider the transformation T: R2 -> R3 defined by T(x,y) = (x-y,x+y,x+2y) Answer the Following a)Find the Standard Matrix A for the linear transformation b)Find T([1 -2]) c) determine if c = [0 is in the range of the transformation T 2 3] Please explain as much as possible this is a test question that I got no points on. Now studying for the final and trying to understand past test questions.
b) More generally, find the matrix of the linear transformation T : R3 → R3 which...
b) More generally, find the matrix of the linear transformation T : R3 → R3 which is u1  orthogonal projection onto the line spanu2. Find the matrix of T. Prove that u3 T ◦ T = T and prove that T is not invertible.
3. Find the linear transformation T : R2 → R2 described geometrically by “first rotate coun-...
3. Find the linear transformation T : R2 → R2 described geometrically by “first rotate coun- terclockwise by 60◦, then reflect across the line y = x, then scale vectors by a factor of 5”. Is this linear transformation invertible? If so, find the matrix of the inverse transformation.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT