(a) Determine if the transformation defined by each of the following standard matrices is injective and/or surjective. i. 1 0 1 1 3 0 2 NLON 4 -2 14 3 11 6 ii. 1 0 -1 221 -4 1 −1 -3 20 -1 -5 0 -1 -3 iii. iv. -2 1520 -4 троф 403 0 0 -2 1 3 1 -2 3 0 -5 1 -2 4 0 -5 -2 4 -4 -4 -1 (b) Which of the above transformations was bijective?

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.6: Introduction To Linear Transformations
Problem 1EQ: 1. Let Ta : ℝ2 → ℝ2 be the matrix transformation corresponding to . Find , where and .
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(a) Determine if the transformation defined by each of the following standard matrices is injective
and/or surjective.
i.
1
0
1
1
3
0 2
NLON
4 -2 14
3
11
6
ii.
1 0 -1
221
-4
1 −1 -3
20
-1 -5
0 -1 -3
iii.
iv.
-2
1520
-4
троф
403
0
0 -2 1
3
1
-2 3
0
-5
1
-2 4
0
-5
-2
4
-4
-4 -1
(b) Which of the above transformations was bijective?
Transcribed Image Text:(a) Determine if the transformation defined by each of the following standard matrices is injective and/or surjective. i. 1 0 1 1 3 0 2 NLON 4 -2 14 3 11 6 ii. 1 0 -1 221 -4 1 −1 -3 20 -1 -5 0 -1 -3 iii. iv. -2 1520 -4 троф 403 0 0 -2 1 3 1 -2 3 0 -5 1 -2 4 0 -5 -2 4 -4 -4 -1 (b) Which of the above transformations was bijective?
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