15. Let A be a 4 x 5 matrix and let U be the reduced row echelon form of A. If 21 -1)

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.4: The Singular Value Decomposition
Problem 26EQ
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n
15. Let A be a 4 x 5 matrix and let U be the reduced
row echelon form of A. If
2
a₁ =
U =
-3
-2
b =
-
10
0
1
0
0
"
0
5
3
4
a₂ =
20
3 0 -2
5
(a) find a basis for N(A).
(b) given that xo is a solution to Ax = b, where
2
3
1
001
0000
and Xo =
=
3
2
0
2
0
(i) find all solutions to the system.
(ii) determine the remaining column vectors
of A.
Transcribed Image Text:al n 15. Let A be a 4 x 5 matrix and let U be the reduced row echelon form of A. If 2 a₁ = U = -3 -2 b = - 10 0 1 0 0 " 0 5 3 4 a₂ = 20 3 0 -2 5 (a) find a basis for N(A). (b) given that xo is a solution to Ax = b, where 2 3 1 001 0000 and Xo = = 3 2 0 2 0 (i) find all solutions to the system. (ii) determine the remaining column vectors of A.
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