The bases for the four subspaces for A when the 3 by 3 matrix is invertible and also for the 3 by 6 matrix
For A,
Row space basis and column space basis is
For B,
Row space basis
Given:
Invertible 3 by 3 matrix A and 3 by 6 matrix
Calculation:
Consider the invertible 3 by 3 matrix A,
Row space basis
Nullspace basis and left nullspace basis both are empty because Z is empty.
Consider 3 by 6 matrix
Row space basis is
Column space basis is
Left nullspace basis is empty because Z is empty
Nullspace basis is
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Introduction to Linear Algebra, Fifth Edition
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