Answered: 9. Let A = 132 -4 253-2 (a) Find a…

9. Let A = 132 -4 253-2 (a) Find a spanning set for Nul A. (b) Find Col A. (c) If T is the linear transformation defined by T(x) = Ax, find its domain, codomain, range, and kernel of T.

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 5CM: Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).

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Question

Question and answer are given, please explain how part c of this problem is obtained.

9. Let A =
132 -4
253 -2
(a) Find a spanning set for Nul A.
(b) Find Col A.
(c) If T' is the linear transformation defined by T(x) = Ax, find its domain, codomain, range,
and kernel of T.

9. (a) spanning set
=
-14
0
= {V₁, V₂}
(c) domain: R4; codomain: R2; range: R2; kernel of T
=
(b) R²
Span {V₁, V₂}

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