2 -3 -7 5 2 -2 [1 0 -2 1 1 0 2 1 1 -2 -4 3 1 -2 1. 1. -1 A 2 0 -4 2 R 0 0 1 3 1 -5 -7 6 2 -7 0 0 Again you may use, without justification, the fact that R is the reduced echelon form of A. Consider the following five vectors in R4: ai a2 az = a5 |1: as (a) Does ag belong to the span of a1, a2, and a5? If not, explain why not; if so, write ag explicitly as a linear combination of a1, a2, and az. (b) Are a1, a2, and az linearly independent? If so, explain why; if not, provide a nontrivial linear depen- dence relation among a1, a2, and a3.
2 -3 -7 5 2 -2 [1 0 -2 1 1 0 2 1 1 -2 -4 3 1 -2 1. 1. -1 A 2 0 -4 2 R 0 0 1 3 1 -5 -7 6 2 -7 0 0 Again you may use, without justification, the fact that R is the reduced echelon form of A. Consider the following five vectors in R4: ai a2 az = a5 |1: as (a) Does ag belong to the span of a1, a2, and a5? If not, explain why not; if so, write ag explicitly as a linear combination of a1, a2, and az. (b) Are a1, a2, and az linearly independent? If so, explain why; if not, provide a nontrivial linear depen- dence relation among a1, a2, and a3.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![2 -3 -7 5 2 -2]
[1 0
-2
1
1
-2 -4 3 1
-2
1
-1
2
|1 -5 -7 6 2 -7
R:
0 0
0 0
-4 2
3
1 1
Again you may use, without justification, the fact that R is the reduced echelon form of A.
Consider the following five vectors in R4:
ai
a2
az =
a5
a6
|1:
(a) Does ag belong to the span of a1, a2, and a5? If not, explain why not; if so, write ag explicitly as a
linear combination of a1, a2, and a5.
(b) Are a1, a2, and az linearly independent? If so, explain why; if not, provide a nontrivial linear depen-
dence relation among a1, a2, and a3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F672bf286-8abe-4b07-9ca1-0d5b2612956c%2Fb6b1be52-9d0e-4984-9167-c1db575f9018%2Fstuojz_processed.png&w=3840&q=75)
Transcribed Image Text:2 -3 -7 5 2 -2]
[1 0
-2
1
1
-2 -4 3 1
-2
1
-1
2
|1 -5 -7 6 2 -7
R:
0 0
0 0
-4 2
3
1 1
Again you may use, without justification, the fact that R is the reduced echelon form of A.
Consider the following five vectors in R4:
ai
a2
az =
a5
a6
|1:
(a) Does ag belong to the span of a1, a2, and a5? If not, explain why not; if so, write ag explicitly as a
linear combination of a1, a2, and a5.
(b) Are a1, a2, and az linearly independent? If so, explain why; if not, provide a nontrivial linear depen-
dence relation among a1, a2, and a3.
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