Question

a. Let →u = (x, y, z) ∈ R^3 and define T : R^3 → R^3...

a. Let →u = (x, y, z) ∈ R^3 and define T : R^3 → R^3 as

T( →u ) = T(x, y, z) = (x + y, 2z − y, x − z)

Find the standard matrix for T and decide whether the map T is invertible.

If yes then find the inverse transformation, if no, then explain why.

b. Let (x, y, z) ∈ R^3 be given T : R^3 → R^2 by T(x, y, z) = (x + 2y, x + y + z)

Find the standard matrix to T and decide whether the map T is invertible.

If yes then find the inverse transformation, if no, then explain why.

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
Let T: R^3----> R^3 where T(x,y,z) = (x-2z,y+z,x+2y) . Is T a one-to-one transformation? Is the...
Let T: R^3----> R^3 where T(x,y,z) = (x-2z,y+z,x+2y) . Is T a one-to-one transformation? Is the range of T R^3 ? Explain
Consider the mapping R^3 to R^3 T[x,y,z] = [x-2z, x+y-z, 2y] a) Show that T is...
Consider the mapping R^3 to R^3 T[x,y,z] = [x-2z, x+y-z, 2y] a) Show that T is a linear Transformation b) Find the Kernel of T Note: Step by step please. Much appreciated.
let let T : R^3 --> R^2 be a linear transformation defined by T ( x,...
let let T : R^3 --> R^2 be a linear transformation defined by T ( x, y , z) = ( x-2y -z , 2x + 4y - 2z) a give an example of two elements in K ev( T ) and show that these sum i also an element of K er( T)
The T: R 4 → R 4 , given by T (x, y, z, w) =...
The T: R 4 → R 4 , given by T (x, y, z, w) = (x + y, y, z, 2z + 1) is a linear transformation? Justify that.
1. Define T : R 2 → R 2 by T(x, y) = (3x + 2y,...
1. Define T : R 2 → R 2 by T(x, y) = (3x + 2y, 5x + y). (a) Represent T as a matrix with respect to the standard basis for R 2 . (b) First, show that B = {(1, 1),(−2, 5)} is another basis for R 2 . Then, represent T as a matrix with respect to B. (c) Using either (a) or (b), find the kernel of T. (d) Is T an isomorphism? Justify your answer....
1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and...
1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and S(x, y, z) = (2y − z, x − z, y + 3x). Use matrices to find the composition S ◦ T. 2. Find an equation of the tangent plane to the graph of x 2 − y 2 − 3z 2 = 5 at (6, 2, 3). 3. Find the critical points of f(x, y) = (x 2 + y 2 )e −y...
Define T:R^2 -> R^2 by T(x,y) = (x+3y, -x+5y) and let B' = {(3,1)^T, (1,1)^T}. Find...
Define T:R^2 -> R^2 by T(x,y) = (x+3y, -x+5y) and let B' = {(3,1)^T, (1,1)^T}. Find the matrix A' for T relative to the basis B'.
Let W = {(x, y, z, w) ∈ R 4 | x − z = 0...
Let W = {(x, y, z, w) ∈ R 4 | x − z = 0 and y + 2z = 0} (a) Find a basis for W. (b) Apply the Gram-Schmidt algorithm to find an orthogonal basis for the subspace (2) U = Span{(1, 0, 1, 0),(1, 1, 0, 0),(0, 1, 0, 1)}.
Let T be the linear transformation from R2 to R2, that rotates a vector clockwise by...
Let T be the linear transformation from R2 to R2, that rotates a vector clockwise by 60◦ about the origin, then reflects it about the line y = x, and then reflects it about the x-axis. a) Find the standard matrix of the linear transformation T. b) Determine if the transformation T is invertible. Give detailed explanation. If T is invertible, find the standard matrix of the inverse transformation T−1. Please show all steps clearly so I can follow your...
Let the linear transformation T: V--->W be such that T (u) = u2 If a, b...
Let the linear transformation T: V--->W be such that T (u) = u2 If a, b are Real. Find T (au + bv) , if u = (x, y) v = (z, w) and uv = (xz-yw, xw + yz) Let the linear transformation T: V---> W be such that T (u) = T (x, y) = (xy, 0) where u = (x, y), with 2, -3. Then, if u = ( 1.0) and v = (0.1). Find the value...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT