
4.1.5 ([Ber14, Ex. 4.2.5]). Fix y € R3 and define T: R3 R3, Tx = 3...
2) Let Let T : R3 - R3 such that T(ij) ,, j 1,2,3. Find the matrix A associated to T in the canonical basis. Find a basis of its kernel and its image. Verify your answers.
2) Let Let T : R3 - R3 such that T(ij) ,, j 1,2,3. Find the matrix A associated to T in the canonical basis. Find a basis of its kernel and its image. Verify your answers.
Find the matrix A' for T relative to the basis B'. T: R3 R3, T(x, y, z) = (x, y, z), B' = {(1, 0, 1), (0, 1, 1), (1, 1, 0)} 0 A 11 1 0 11 X
Find the matrix A' for T relative to the basis B'. T: R3 R3, T(x, y, z) = (x, y, z), B' = {(1, 0, 1), (0, 1, 1), (1, 1, 0)} 1 0 0 1 A' = 1 1 1 0 X
Find the matrix A' for T relative to the basis B'. T: R3 → R3, T(x, y, z) = (x, y, z), B' = {(1, 0, 1), (0, 1, 1), (1, 1, 0)} A' = 11 JITE
Suppose A is the matrix for T: R3 → R3 relative to the standard basis. Find the matrix A' for T relative to the basis B': 3 -2 A 4 2 5 B' = {(1,1, -1), (1,-1,1),(-1,1,1)}
Please show work and explain.
Suppose A is the matrix for T: R3 R3 relative to the standard basis. Find the matrix A' for T relative to the basis B': 3 -1 -2 4 A= 1 5 B' = {(1,1, -1),(1,-1,1),(-1,1,1)}
Problem #7: suppose that vectors in R3 are denoted by 1 x 3 matrices and define T: R3 R3 by 3 7([xi x2 x3]) = [x1 x2 x3]| 4 3 0 0] 8 Find a basis for the range of T. Problem #7: Select
2. (8 marks] Consider the linear transformation T:R3 R2 TX,Y, 2) = (+y-2, -1-y+z). (a) Show that the matrix (TE.Es representing T in the standard bases of R3 and R² is of the form TEE 1 -1 1 -1 -1 1 (b) Find a basis of the null space of T and determine the dimension of this space. (c) Find a basis of the range of T and determine the dimension of the range of T. (d) Is T Onto?...
16. Let x and y be vectors in R3 and define the skew- symmetric matrix A, by 10-X3 X2 A = X3 0 -X1 I-X2 x 0 (a) Show that x x y = Axy. (b) Show that y x x = Amy.
Let T: R3 → R2 T(x, y, z) = (x + y,y+z) a. Is T a linear transformation? b. Find the matrix A of T C. Find the dimension of NUT and image T