) 3ri - 512- 370rs ] Let T: R³ → R“ be the linear transformation given by (E)-| 2811 — 19г2 — 132гз 47x1 + 73x2 + 198x3 T -23x1 + 17x2 + 114.x3 (a) Find a basis for the kernel of T and determine whether T is injective. (b) Find a basis for the range of T and determine whether T is surjective.

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 6CM: Let T:R4R2 be the linear transformation defined by T(v)=Av, where A=[10100101]. Find a basis for a...
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Let T: R → R“ be the linear transformation given by
(E)-
2811 — 19г2 — 132г3
47x1 + 73x2 + 198r3
-23.r1 + 17x2 + 114r3
8371 — 51гр — 37073
T
(a) Find a basis for the kernel of T and determine whether T is injective.
(b) Find a basis for the range of T and determine whether T is surjective.
3.
Transcribed Image Text:Let T: R → R“ be the linear transformation given by (E)- 2811 — 19г2 — 132г3 47x1 + 73x2 + 198r3 -23.r1 + 17x2 + 114r3 8371 — 51гр — 37073 T (a) Find a basis for the kernel of T and determine whether T is injective. (b) Find a basis for the range of T and determine whether T is surjective. 3.
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