If A is a 25 x 5 matrix and T is a transformation defined by T(x) = A, what is the codomain of T? OR 25 OR5 Defend your response.

Suppose T transposes every 2 by 2 matrix M. Try to find a matrix A which gives AM = MT. Show that no matrix A will do it. To professors: Is this a linear transformation that doesn't come from a matrix? The matrix should be 4 by 4!

A firm's total revenue function takes the form cQ2 + dQ. It is known that TR = 402 when Q = 3 and TR = 1098 when Q = 9. (a) Show that this information may be expressed as Ax = b where x = [c, d]¹, b = [402, 1098] and A is a 2x2 matrix which should be stated. (b) Use the matrix inverse method to work out the values of c and d, and hence write down the demand equation. (a) The coefficient matrix is (b) c= -2, d = 140 and the demand equation is P=Q+

Consider the following matrix. Show that Col(B) and Null(B^T) are orthogonal to each other.