Consider the following matrix A: 2 2 2 3 8 8 -3 -6 -4 1 0 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=b₁. A = b1 = b2 = 4 6 -10 -4 ܐ ܬ ܩ ܘ ~ ∞0 m -8 b3 = b₁ is in im(a): 0 A0 =b₁ 0 b2 is in im(a): 1981- A 0 =b₂ b3 is in im(a): 0 A0 =b3

Elementary Linear Algebra (MindTap Course List)
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Chapter4: Vector Spaces
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Consider
the following matrix A:
2 2 2
388
-3 -6 -4
1 0 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=b₁.
A =
b₁
=
b₂ =
b3 =
4
- 10
-4
-9
-6
0
-2
-8
8
∞03
b₁ is in im(a):
0
A0 =b₁
0
b2 is in im(a):
0
A0=b₂
0
b3 is in im(a):
0
A0 =b3
0
Transcribed Image Text:Consider the following matrix A: 2 2 2 388 -3 -6 -4 1 0 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=b₁. A = b₁ = b₂ = b3 = 4 - 10 -4 -9 -6 0 -2 -8 8 ∞03 b₁ is in im(a): 0 A0 =b₁ 0 b2 is in im(a): 0 A0=b₂ 0 b3 is in im(a): 0 A0 =b3 0
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