1 2 -1 Let A and assume that %3D 2 -1 1 -2 10 0 -2 1 -1 011-1 B is row equivalent to the matrix C= 0 0 0 0 0 0 2 -2 -1-1 1 Use the above to answer the following questions. 7.1Find a basis for the nullspace of A. 7.2Find a basis for the column space of A. 7.3Find the rank and nullity of A.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.6: The Algebra Of Matrices
Problem 13E
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Question
1
2 -1
Let A
and assume that
%3D
1
2 -1
0 -1
-2
10 0
0 11-1
0 0 0
0 0 0
1
1 -1
is row equivalent to the matrix C=
-2
B =
2 -2
1 -1
1
Use the above to answer the following questions.
7.1Find a basis for the nullspace of A.
7.2Find a basis for the column space of A.
7.3Find the rank and nullity of A.
Transcribed Image Text:1 2 -1 Let A and assume that %3D 1 2 -1 0 -1 -2 10 0 0 11-1 0 0 0 0 0 0 1 1 -1 is row equivalent to the matrix C= -2 B = 2 -2 1 -1 1 Use the above to answer the following questions. 7.1Find a basis for the nullspace of A. 7.2Find a basis for the column space of A. 7.3Find the rank and nullity of A.
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