W = {y= 2x1 - 3x₂ + x3 -x₁ + 4x2 - 2x3: X1, X2, X3 real}. 2x1 + x2 + 4x3 Exhibit a (3 x 3) matrix A such that W = R(A). Conclude that W is a subspace of R³.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.5: Subspaces, Basis, Dimension, And Rank
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Linear algebra: please solve q42 correctly and handwritten 

42. Let
W = {y =
2x13x2 + x3
-x₁ +4x22x3
2x1 + x2 + 4x3
X1, X2, X3 real).
Exhibit a (3 x 3) matrix A such that W = R(A).
Conclude that W is a subspace of R³.
43. Let
X1
Transcribed Image Text:42. Let W = {y = 2x13x2 + x3 -x₁ +4x22x3 2x1 + x2 + 4x3 X1, X2, X3 real). Exhibit a (3 x 3) matrix A such that W = R(A). Conclude that W is a subspace of R³. 43. Let X1
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