(a) Find the determinant of the matrix A below. 1 0 -1 2 2 1 A -1 0 -1 2 0 -4 8 4 (b) Find the matrix associated to the linear transformation T below, with respect to the standard basis {e1, e2, e3} of R³. T: (x, y, z) → (-x, z, y) where x, y, z E R (c) Explain whether the linear transformation in part (b) is invertible or not. (d) With the basis B for R3 below, find [T]B, the matrix associated to the linear transfor- mation T from part (b) with respect to B. B = {(1,0,0), (0, 1, 1), (0, – 1, 1)}. %3D
(a) Find the determinant of the matrix A below. 1 0 -1 2 2 1 A -1 0 -1 2 0 -4 8 4 (b) Find the matrix associated to the linear transformation T below, with respect to the standard basis {e1, e2, e3} of R³. T: (x, y, z) → (-x, z, y) where x, y, z E R (c) Explain whether the linear transformation in part (b) is invertible or not. (d) With the basis B for R3 below, find [T]B, the matrix associated to the linear transfor- mation T from part (b) with respect to B. B = {(1,0,0), (0, 1, 1), (0, – 1, 1)}. %3D
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 12CM
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Question
![3. (a) Find the determinant of the matrix A below.
1
0 -1 2
2
1
A
-1 0 -1 2
4 0 -4 8
(b) Find the matrix associated to the linear transformation T below, with respect to the
standard basis {e1, e2, e3} of R³.
T: (x,y, z) → (-x, z, y) where x, y, z E R
(c) Explain whether the linear transformation in part (b) is invertible or not.
(d) With the basis B for R³ below, find [T]B, the matrix associated to the linear transfor-
mation T from part (b) with respect to B.
B = {(1,0, 0), (0, 1, 1), (0, – 1, 1)}.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5ea8dc3-9812-419a-a20e-59637a068d91%2Fb3695e3e-704f-46e1-b3e8-0ec82476b54a%2F5vv37ad_processed.png&w=3840&q=75)
Transcribed Image Text:3. (a) Find the determinant of the matrix A below.
1
0 -1 2
2
1
A
-1 0 -1 2
4 0 -4 8
(b) Find the matrix associated to the linear transformation T below, with respect to the
standard basis {e1, e2, e3} of R³.
T: (x,y, z) → (-x, z, y) where x, y, z E R
(c) Explain whether the linear transformation in part (b) is invertible or not.
(d) With the basis B for R³ below, find [T]B, the matrix associated to the linear transfor-
mation T from part (b) with respect to B.
B = {(1,0, 0), (0, 1, 1), (0, – 1, 1)}.
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