Finding a Matrix for a Linear Transformation In Exercises 1–12, find the matrix A′ for T relative to the basis B′.
T: R3→R3, T(x, y, z) = (x, x + 2y, x + y + 3z), B′ = {(1, −1, 0), (0, 0, 1), (0, 1, −1)}
Finding a Matrix for a Linear Transformation In Exercises 1–12, find the matrix A′ for T...
12: Find a basis B for R', such that the matrix for the linear transformation T: R' R', T(x,y,z)-(2x-2z,2y-2z,3x-3z) relative to B is diagonal. 12: Find a basis B for R', such that the matrix for the linear transformation T: R' R', T(x,y,z)-(2x-2z,2y-2z,3x-3z) relative to B is diagonal.
Find the standard matrix for the linear transformation T. T(x, y) = (3x + 2y, 3x – 2y) Submit Answer [-70.71 Points] DETAILS LARLINALG8 6.3.007. Use the standard matrix for the linear transformation T to find the image of the vector v. T(x, y, z) = (8x + y,7y - z), v = (0, 1, -1) T(v)
Find the standard matrix for the linear transformation T. T(x, y, z) = (x - 2z, 2y = z) 11
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) = (-3x + 2y – 32, 2x - 62, -* - 2y – z) -4 0 0 0 -4 B = 0 0 X Need Help? Read It Watch It Talk to a Tutor
Finding the Nullity and Describing the Kernel and Range In Exercises 33–40, let T: R3→R3 be a linear transformation. Find the nullity of T and give a geometric description of the kernel and range of T. T is the reflection through the yz-coordinate plane: T(x, y, z) = (−x, y, z)
29&30 please 3 -23 4 3-2 25. 3 4926. |0 1 1 0 0-2 1 2-5 Finding a Basis In Exercises 27-30, find a basis B for the domain of T such that the matrix for T relative to B is diagonal. 27. T: R2→R-T(x, y) = (x + y, x + y) 28. T: R3→R, Tu, y, z) (-2x +2y -3z, 2r y -6z. 2y) a + (af+ 2b)s 29. T: Pi-Pi T(a + bx) 30. T: P㈠Pg Tle...
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
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
Consider the linear transformation T: "R" whose matrix A relative to the standard basis is given. A=[1:2] (a) Find the eigenvalues of A. (Enter your answers from smallest to largest.) (11, 12) = 2,3 |_) (b) Find a basis for each of the corresponding eigenspaces. B = X B2 = = {I (c) Find the matrix A' for T relative to the basis B', where B'is made up of the basis vectors found in part (b). A=
linear algebra Find the standard matrix for the linear transformation T. T(x, y, z) = (6x – 8z, 8y - z) BE