2. Let A be a 4 x 5 matrix and let U be the reduced row echelon form of A. If 2 1 2 a₁ = a2 = -3 3 2 1 0 2 0 0 1 3 0 -2 U = 0 0 0 1 5 0 0 0 0 0 (a) find a basis for N(A). (b) given that xo is a solution to Ax = b, where 3 2 5 b= 3 and Xo= 0 2 0 (i) find all solutions to the system. (ii) determine the remaining column vectors of A. C Cl .

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 3AEXP
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2.
Let A be a 4 x 5 matrix and let U be the reduced
row echelon form of A. If
2
1
2
a₁ =
a2 =
-3
3
2
1
0
2
0
0
1
3
0
-2
U =
0
0
0
1
5
0
0
0
0
0
(a) find a basis for N(A).
(b) given that xo is a solution to Ax = b, where
3
2
5
b=
3
and Xo=
0
2
0
(i) find all solutions to the system.
(ii) determine the remaining column vectors
of A.
C
Cl
.
Transcribed Image Text:2. Let A be a 4 x 5 matrix and let U be the reduced row echelon form of A. If 2 1 2 a₁ = a2 = -3 3 2 1 0 2 0 0 1 3 0 -2 U = 0 0 0 1 5 0 0 0 0 0 (a) find a basis for N(A). (b) given that xo is a solution to Ax = b, where 3 2 5 b= 3 and Xo= 0 2 0 (i) find all solutions to the system. (ii) determine the remaining column vectors of A. C Cl .
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