Without mUltiplying matrices, find bases for the row and column spaces of A: [ 1 2] [3 0

Chapter 3, Problem 23

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Without mUltiplying matrices, find bases for the row and column spaces of A: [ 1 2] [3 0 3] A= ~ ~ 1 1 2 . How do you know from these shapes that A cannot be invertible?

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