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Construct a matrix whose column space contains (1, 1, 5) and (0, 3, 1) and whose nullspace contains (1, 1, 2).

Construct a matrix whose column space contains (1, 1, 5) and (0, 3, 1) and whose nullspace contains (1, 1, 2).

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 69E: Consider an mn matrix A and an np matrix B. Show that the row vectors of AB are in the row space of...
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I need help with this please:

A) Construct a matrix whose column space contains (1, 1, 5) and (0, 3, 1) and whose
nullspace contains (1, 1, 2). 

B) If AB = 0 then the column space of B is contained in the __ of A. Why?

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