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## Use matrix B in Problem 2.26 to illustrate Theorem 2.11 parts (iii) and (iv). Problem 2.26 Let…

Use matrix B in Problem 2.26 to illustrate Theorem 2.11 parts (iii) and (iv).

Problem 2.26

Let

(a) Find a matrix C such that AB = CB. Is C unique?

(b) Find a vector x such that Ax = 0. Can you do this for B?

Theorem 2.11

Theorem 2.11

(i) If A and B are n x n, then

(ii) If A is n x p and B is p x n, then

Note that in (2.87) n can be less than, equal to, or greater than p

(iii) If A is n x p, then

where  is the ith column of A.

(iv) If A is n x p, then

where  is the ith row of A.

(v) If A= (aij) is an n p matrix with representative element aij, then

(vi) If A is any n x n matrix and P is any n x n nonsingular matrix, then

(vii) If A is any n x n matrix and C is any n x n orthogonal matrix, then

(viii) If A is n x p of rank r and  is a generalized inverse of A, then

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