Question

Suppose A is the matrix for T: R3 → R3 relative to the standard basis. Find...

Suppose A is the matrix for T: R3 → R3 relative to the standard basis.

Find the diagonal matrix A' for T relative to the basis B'. A = −1 −2 0 −1 0 0 0 0 1 , B' = {(−1, 1, 0), (2, 1, 0), (0, 0, 1)}

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find a basis B for the domain of T such that the matrix for T relative...
Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R3 → R3: T(x, y, z) = (−5x + 2y − 3z, 2x − 2y − 6z, −x − 2y − 3z)
Find a basis B for the domain of T such that the matrix for T relative...
Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R3 → R3: T(x, y, z) = (−4x + 2y − 3z, 2x − y − 6z, −x − 2y − 2z) B =
Find a basis B for the domain of T such that the matrix for T relative...
Find a basis B for the domain of T such that the matrix for T relative to B is diagonal. T: R3 → R3: T(x, y, z) = (−5x + 2y − 3z, 2x − 2y − 6z, −x − 2y − 3z) B = Incorrect: Your answer is incorrect.
7.18) Find the matrix of the cross product transformation Ca: R3-->R3 with respect to the standard...
7.18) Find the matrix of the cross product transformation Ca: R3-->R3 with respect to the standard basis in the following cases: 1) a = e1 2) a = e1 + e2 + e3
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.
Find the matrix for a linear map T: R4 -> R3 given by T([a, b, c,...
Find the matrix for a linear map T: R4 -> R3 given by T([a, b, c, d]) = [-c+d, a-b+4c, 3b+2d].
Find the coordinates of e1 e2 e3 of R3 in terms of [(1,0,0)T , (1,1,0)T ,...
Find the coordinates of e1 e2 e3 of R3 in terms of [(1,0,0)T , (1,1,0)T , (1,1,1)T ] of R3,, and then find the matrix of the linear transformation T(x1,, x2 , x3 )T = [(4xx+ x2- x3)T , (x1 + 3x3)T , (x2 + 2x3)T with respect to this basis.
10 Linear Transformations. Let V = R2 and W = R3. Define T: V → W...
10 Linear Transformations. Let V = R2 and W = R3. Define T: V → W by T(x1, x2) = (x1 − x2, x1, x2). Find the matrix representation of T using the standard bases in both V and W 11 Let T :R3 →R3 be a linear transformation such that T(1, 0, 0) = (2, 4, −1), T(0, 1, 0) = (1, 3, −2), T(0, 0, 1) = (0, −2, 2). Compute T(−2, 4, −1).
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.
In this question, as usual, e1, e2, e3 are the standard basis vectors for R 3...
In this question, as usual, e1, e2, e3 are the standard basis vectors for R 3 (that is, ej has a 1 in the jth position, and has 0 everywhere else). (a) Suppose that D is a 3 × 3 diagonal matrix. Show that e1, e2, e3 are eigenvectors of D. (b) Suppose that A is a 3 × 3 matrix, and that e1, e2, and e3 are eigenvectors of A. Is it true that A must be a diagonal...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT