Consider the following matrix A: [0 1 -1 A = 0 5 -5 1 -1 -3 For each of the following vectors, determine whether the vector is in the image of A. If so, demonstrate this by providing a vector x so that Ax=b;. b₁ b2 = = b3 = -4 -20 -5 2 7 -10 0 5 b₁ is in im(a): 0 A0 =b₁ 0 b2 is in im(a): 0 A0=b₂ 0 b3 is in im(a): 0 OOO A0 =b3 0
Consider the following matrix A: [0 1 -1 A = 0 5 -5 1 -1 -3 For each of the following vectors, determine whether the vector is in the image of A. If so, demonstrate this by providing a vector x so that Ax=b;. b₁ b2 = = b3 = -4 -20 -5 2 7 -10 0 5 b₁ is in im(a): 0 A0 =b₁ 0 b2 is in im(a): 0 A0=b₂ 0 b3 is in im(a): 0 OOO A0 =b3 0
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter10: Matrices
Section10.CR: Chapter 10 Review
Problem 9CR
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Transcribed Image Text:Consider the following matrix A:
01 -1
A = 0 5 -5
1 -1 -3
For each of the following vectors, determine whether the vector is in the image of A. If so, demonstrate this by providing a vector x so that Ax=b¡.
b₁
b2
=
=
b3 =
-4
-20
-5
2
7
-10
0
0
5
b₁ is in im(a):
0
A0 =b₁
0
b2 is in im(a):
0
A0 =b₂
0
b3 is in im(a):
A0=b3
0.
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