The basic definition of matrix multiplication A B tells us to multiply rows of A times columns of B. Remarkably, if you suitably interpret the operation, you can also compute A B by multiplying columns of A times rows of B! Suppose A is an m x n matrix with columns C1,... , cn. Suppose B is an n × p matrix with rows r1... , rn. Then we claim that
AB = c1r1+c2r2 +------+cnrn. (1.14)
where each summand is a matrix of size m × p.
(a) Verify the particular case

does agree with the usual method for computing the matrix product.
(b) Use this method to compute the matrix products
(i)

(ii)

(iii)

and verify that you get the same answer as the traditional method.
(c) Explain why (1.13) is a special case of (1.14).
(d) Prove that (1.14) gives the correct formula for the matrix product.

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