Problem:(adsbygoogle = window.adsbygoogle || []).push({}); Explain why the columns of [itex]A^2[/itex] span [itex]\mathbb{R}^n[/itex] whenever the colums of A are linearly independent.

By the theorem given in that section of the text, it is a logically equivalent fact that if the columns of [itex]A^2[/itex] are linearly independent, then they span [itex]\mathbb{R}^2[/itex] or

[tex]\mathbb{R}^2=Span( \vec{a}_1 , \vec{a}_2 ) [/tex].

How do I expand this definition from [itex]\mathbb{R}^2[/itex] to [itex]\mathbb{R}^n[/itex]?

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# Homework Help: Lin Alg proof problem

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