For the matrix 2 -3 5 A = -2 -2 -6 3 -3 consider the set S = {b€R³ : for some x E R}. = Ax Let's show that S is indeed a subspace of R. i) S contains the zero-vector. Since 0 = Ax where X = <1,3,-2>

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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For the matrix
1
2
-3
5
A :
-2 -2
2
-6
3
3
-3 9
consider the set
S = {b E R´ : b = Ax_ for some
X E R4
Let's show that S is indeed a subspace of R.
i) S contains the zero-vector. Since | 0 = Ax where
X =
<1,3,-2>
Recall: the Maple syntax for a vector in R4 is < a,b,c,d >.
Transcribed Image Text:For the matrix 1 2 -3 5 A : -2 -2 2 -6 3 3 -3 9 consider the set S = {b E R´ : b = Ax_ for some X E R4 Let's show that S is indeed a subspace of R. i) S contains the zero-vector. Since | 0 = Ax where X = <1,3,-2> Recall: the Maple syntax for a vector in R4 is < a,b,c,d >.
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