Consider the following matrix A: 22-8 A = -2 0 4 -1 1 0 For each of the following vectors, determine whether the vector is in the column space of A. If so, demonstrate this by providing a vector x so that Ax=b;. b₁ is in col(a): b₁ = 5 10 b2 b3 = -12 6 -2 = 0 A 0 0 b₁ b2 is in col(a): A b₂ b3 is in col(a): A0 =b3
Consider the following matrix A: 22-8 A = -2 0 4 -1 1 0 For each of the following vectors, determine whether the vector is in the column space of A. If so, demonstrate this by providing a vector x so that Ax=b;. b₁ is in col(a): b₁ = 5 10 b2 b3 = -12 6 -2 = 0 A 0 0 b₁ b2 is in col(a): A b₂ b3 is in col(a): A0 =b3
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:Consider the following matrix A:
2 2-8
A = -2 0 4
-1 1 0
For each of the following vectors, determine whether the vector is in the column space of A. If so, demonstrate this by providing a vector x so that Ax=b₁.
5
b₁ =
b2
||
=
b3 =
ܕܐ ܗ
10
-12
0
NOT
b₁ is in col(a):
0
A0 =b₁
0
b2 is in col(a):
0
A0=b₂
0
b3 is in col(a):
0
A0 =b3
0
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