Define the linear transformation T by T(x) = AX. 3 2 -1 -1 -2 1. A = -4 -3 -1 -3 -1 4 (a) Find the kernel of T. (If there are an infinite number of solutions use t as your parameter.) ker(7) = . (b) Find the range of T.

Define the linear transformation T by T(x) = AX. 3 2 -1 -1 -2 1. A = -4 -3 -1 -3 -1 4 (a) Find the kernel of T. (If there are an infinite number of solutions use t as your parameter.) ker(7) = . (b) Find the range 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 4CM

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Question

Define the linear transformation T by T(x) = Ax.
3
2
-1
-1 -2
1
1
A =
-4 -3 -1
-3
1.
2
-1
(a) Find the kernel of T. (If there are an infinite number of solutions use t as your parameter.)
ker(T) =
(b) Find the range of T.
O R3
span{(1, 0, 0, -1), (0, 1, 0, 0), (0, о, 1, —1)}
O span{(1, 0, 0, -1), (0, 1, 0, 0)}
span{(1, 0, 0, —-1), (0, о, 1, —1)}
R4

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