推 hsuanboy :謝謝大大!~~ 10/14 02:09
※ 引述《hsuanboy (壓力)》之銘言：
: a(A+B) = aA + aB 乘法對加法的分配律
: 請問該如何證明呢 謝謝!
Let C = A + B be a n by n matrix over a field F, where c_ij = a_ij + b_ij.
Let a in F. Then a(A+B) = [a c_ij]
= [a(a_ij + b_ij)]
= a [a_ij] + a [b_ij].
= a A + a B.
This completes the proof.
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