(a) Determine if the transformation defined by each of the following standard matrices is injective and/or surjective. i. 1 15 4 1 3 1 5 1 2 0 1 1 -3 5 2 1 ii. 1200 -2 -3 5 3 -4 -4 4 4 iii. 1 0 -3 -1 6 0 1 -4 -2 12 4 1 5 15 -27 0 0 -5 -5 15 iv. -5 -10 5 20 -3 -6 4 15 2 4 -2 -8 -5 -10 2 11 (b) Which of the above transformations was bijective?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(a) Determine if the transformation defined by each of the following standard matrices is injective
and/or surjective.
i.
1
15
4 1
3
1
5
1 2
0
1 1
-3
5 2
1
ii.
1200
-2
-3
5
3
-4
-4
4 4
iii.
1 0
-3
-1 6
0 1
-4
-2 12
4 1 5
15 -27
0 0 -5
-5
15
iv.
-5 -10 5 20
-3 -6 4 15
2 4 -2 -8
-5 -10 2 11
(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 15 4 1 3 1 5 1 2 0 1 1 -3 5 2 1 ii. 1200 -2 -3 5 3 -4 -4 4 4 iii. 1 0 -3 -1 6 0 1 -4 -2 12 4 1 5 15 -27 0 0 -5 -5 15 iv. -5 -10 5 20 -3 -6 4 15 2 4 -2 -8 -5 -10 2 11 (b) Which of the above transformations was bijective?
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