Construct a matrix whose column space contains (1, 1, 0) and (0, 1, 1) and whose nullspace contains (1, 0, 1) and (0, 0, 1).

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter7: Systems Of Equations And Inequalities
Section7.7: Solving Systems With Inverses
Problem 4SE: Can a matrix with an entire column of zeros have an inverse? Explain why or why not.
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Construct a matrix whose column space contains (1, 1, 0) and (0, 1, 1) and whose nullspace contains (1, 0, 1) and (0, 0, 1).

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Step 1

Column space: A space spanned by the columns of a matrix is called the column space of a matrix. The

column space forms a subspace.

Null space: The set of solutions of a matrix equation such that AX=0 is called the null space of the

matrix A and this space forms a subspace.

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