Linear Algebra: help session on matrix multiplication and index calculation, 1-25-18, part 1

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For the proof at 3:23 isn’t showing n=2 redundant? If you just state n=1, (A1)ij=(A1)ij, then by using the induction step it follows for n=1+1=2 that (A1+A2)ij=(A1)ij+(A2)ij

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