If A is an m x n matrix and C is an r x s matrix what must b

If A is an m x n matrix and C is an r x s matrix, what must be the dimensions of B in order for the product ABC to be defined? Write an expression for the (i,j)th element of ABC in terms of the elements of A, B, and C.

Solution

The dimension of B should be n x r because in matrix multiplication, the number of columns in the matrix on the left must be equal to the number of rows in the matrix on the right.

Expression ABCij = Ai0j1 Bi1j2 Ci2j3 + Ai1j2 Bi2j3 Ci3j4 + ......