Prove: If k !=0, then A and kA have the same rank.(adsbygoogle = window.adsbygoogle || []).push({});

Given:

k is in the set of all Reals.

proof:

WOLOG let A be an M X N matrix

Assume m < n

=> the max rank(A) can be is m. (i.e. the row space and the column space)

=> the max the rank(kA) can be is also m, because multiplying a matrix by a constant does not change the dimensions of the matrix

=>

# of leading variables stays the same for A and KA

=>

Rank(A)=Rank(KA)..

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# Homework Help: Help with proof

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