Let A 3 be the ring Mn (K) with matrix addition and multiplication and A, B € Mn (K).

The Binomial theorem

m

(A + B)" = (m Am-kBk

k=0\/

does not apply to matrices in general. First, give a counterexample with 2x2-

Matrices in which the binomial theorem is not satisfied. Why is it that the Does

the teaching not apply in general?

The length /v] of a vector v = (v1 v2) € R2 can be calculated as [v] =Vv2 + v3.

(3 Points)

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