) 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.
) 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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