Consider the following matrix A: 3-3-3 3-1-7 A = 2-3 3 2 -3 -2 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. b₁ = b3 = -6 -18 8 -2 3 15 -10 0 ܬ 5 -3 6 b₁ is in col(a): 0 A0 =b₁ 0 b2 is in col(a): 0 A0=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
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Consider the following matrix A:
3 -3 -3
3 -1 -7
2-3 3
A =
=
2
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
||
b₂ =
b3 =
-3 -2
-6
-18
8
-2
3
15
-10
0
LO
-3
6
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
Transcribed Image Text:Consider the following matrix A: 3 -3 -3 3 -1 -7 2-3 3 A = = 2 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 || b₂ = b3 = -3 -2 -6 -18 8 -2 3 15 -10 0 LO -3 6 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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