(a) Compute the standard matrix for the linear transformation S: R4 → R³ given by S x = 3x+2y-3z+5w -3x+6y-4z - 6 w -5x-4y 4 w พ (b) Let T R³ → R³ be the linear transformation given by the standard matrix 5 -1 -5 0 3 1 -5 -4 1 4 -2 ]) Compute T •((÷)) 0 by using the values of transformed standard basic vectors.

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
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(a) Compute the standard matrix for the linear transformation S: R4 → R³ given by
S
x
=
3x+2y-3z+5w
-3x+6y-4z - 6 w
-5x-4y 4 w
พ
(b) Let T R³ → R³ be the linear transformation given by the standard matrix
5
-1 -5
0
3
1
-5 -4
1
4
-2
])
Compute T
•((÷))
0
by using the values of transformed standard basic vectors.
Transcribed Image Text:(a) Compute the standard matrix for the linear transformation S: R4 → R³ given by S x = 3x+2y-3z+5w -3x+6y-4z - 6 w -5x-4y 4 w พ (b) Let T R³ → R³ be the linear transformation given by the standard matrix 5 -1 -5 0 3 1 -5 -4 1 4 -2 ]) Compute T •((÷)) 0 by using the values of transformed standard basic vectors.
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