3. (a) Find the determinant of the matrix A below. 1 0 -1 2 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 € R (c) Explain whether the linear transformation in part (b) is invertible or not.
3. (a) Find the determinant of the matrix A below. 1 0 -1 2 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 € R (c) Explain whether the linear transformation in part (b) is invertible or not.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 55EQ
Related questions
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]g, the matrix associated to the linear transfor-
mation T from part (b) with respect to B.
В 3 {(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%2Fa24cbfc3-0ade-466f-a4a0-f98e495a1180%2Fovio9jm_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]g, the matrix associated to the linear transfor-
mation T from part (b) with respect to B.
В 3 {(1,0, 0), (0, 1, 1), (0, —1, 1)}.
||
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