2. (a) Let T be the linear transformation which projects R^3
orthogonally onto the plane 2x+3y+4z = 0. What are the eigenvalues
and associated eigenspaces of T? Justify your answer.
(b) Does the linear transformation described in (a) have an
inverse? Why, or why not?
2. (a) Let T be the linear transformation which projects R^3 orthogonally onto the plane 2x+3y+4z = 0. What are the eigenvalues and associated eigenspaces of T? Justify your answer. (b) Does the linea...
2. (a) Let T be the linear transformation which projects R3 orthogonally onto the plane 2x+3y+4a-0. what are the eigenvalues and associated eigenspaces of T? Justify your answer (b) Does the linear transformation described in (a) have an inverse? Why, or why not? [10 pts]
2. (a) Let T be the linear transformation which projects R3 orthogonally onto the plane 2x+3y+4a-0. what are the eigenvalues and associated eigenspaces of T? Justify your answer (b) Does the linear transformation described in...
Problem 3. Let T R2 -R be a linear transformation, with associated standard matrir A. That is [T(TleAl, where E = (e1, ē2) is the standard basis of R2. Suppose B is any basis for R2 a matrix B such that [T()= B{v]B. This matric is called the the B-matrix of T and is denoted by TB, (2) What is the first column of T]s (3) Determine whether the following statements are true or (a) There erists a basis B...
5. (8 pts) Suppose B is a 4 x 5 matrix, and the associated linear transformation T(E) Bd, is onto. (a) (3) Find dim Nul(B) (b) (2) Does Ba 5 have a unique solution for every B (c) (3) Give a geometric interpretation to the solution set of Bt- 0
5. (8 pts) Suppose B is a 4 x 5 matrix, and the associated linear transformation T(E) Bd, is onto. (a) (3) Find dim Nul(B) (b) (2) Does Ba 5...
1 4 bea linear/matrix transformation such that Let T: 3 Fi 1 4 1 T 1 1 C 6 h 3 Use the fact that T is linear to find the standard matrix [T of T and find T 1 Find a match for each of the following questions or choose NO MATCH if you can't find a match. What is the domain of T? What is the codomain of T? 4 4 How many rows does [T] have? How...
s={(8.60) :) :) is a basis of M3x2(R)? (d) (1 point) The set = {(1 9:(. :) : 6 1) (1 1) (1 :) :()} is linearly independent. (e) (1 point) For a linear transformation A:R" + Rd the dimension of the nullspace is larger than d. (f) (1 points) Let AC M4x4 be a diagonal matrix. A is similar to a matrix A which has eigenvalues 1,2,3 with algebraic multiplicities 1,2, 1 and geometric multiplicities 1,1, 1 respectively. 8....
Let k be an integer such that the vectors and 3 are linearly dependent. What must be the value of - 1, 2 [1] [-1 Answer: 1 Incorrect. Try again Next page bus page 1 1 1] Let A = 1 -1 2 and x = 22 Lo -2 1] [3] [1] Let p = 2.9= 0 and r = 2 Lo] How many of the systems Az = p.Az =q, Az = r have at least one solution? (1)...
(a) Let T: R2 + R2 be counter clockwise rotation by 7/3, i.e. T(x) is the vector obtained by rotating x counter clockwise by 7/3 around 0. Without computing any matrices, what would you expect det (T) to be? (Does T make areas larger or smaller?) Now check your answer by using the fact that the matrix for counter clockwise rotation by is cos(0) - sin(0)] A A= sin(0) cos(0) (b) Same question as (a), only this time let T...