Let V be the subspace of ℝ4 spanned by the columns of the matrix  A=[1 2 3 −2 3 8 5 1 −3 −3 −4 −5 ]  (a) Find a basis of V. (b) What is the dimension of V (c) Extend the basis of V to a basis of ℝ4.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Let V be the subspace of ℝ4 spanned by the columns of the matrix
 
A=[
1 2 3 −2 3 8 5 1 −3 −3 −4 −5 ]
 
(a) Find a basis of V.

(b) What is the dimension of V

(c) Extend the basis of V to a basis of ℝ4.

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