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Matrix dimensions. Suppose A is an m×n matrix, and B is a p×q matrix. For each of the following equations, give the conditions on m, n, p, q under which it makes sense. For example, A = B requires that m = p and n = q. (a) ATB = I. (b) AB = 0. (c) AB = BA. (d) AT = [B I]. (e) [A B] = I.

Matrix dimensions. Suppose A is an m×n matrix, and B is a p×q matrix. For each of the following equations, give the conditions on m, n, p, q under which it makes sense. For example, A = B requires that m = p and n = q. (a) ATB = I. (b) AB = 0. (c) AB = BA. (d) AT = [B I]. (e) [A B] = I.

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Matrix dimensions. Suppose A is an m × n matrix, and B is a p × q matrix. For each of the following equations, give the conditions on m , n , p , q under which it makes sense. For example, A = B requires that m = p and n = q . (a) A T B = I . (b) A B = 0 . (c) A B = B A . (d) A T = [ B I ] . (e) [ A B ] = I .

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