3. . Let T (C)-[ a) T(T(X))= AX b) T₂(T2(X)) = BX == x₁ + x2 2x+7x2 x₁ & T x+5x2 x+3x2 Find the matrices A and B such that:

Show that no 22 matrices A and B exist that satisfy the matrix equation. AB-BA=1001.

Let X1,X2,X3 and b be the column matrices below. X1=[101], X2=[110], X3=[011] and b=[123] Find constants a, b, c and c such that aX1+bX2+cX3=b

To find the product matrix AB. the number of _______________ of A must be the same as the number of _________ of B.

Let A be an nn matrix in which the entries of each row sum to zero. Find |A|.

Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.