If A and B are 8x3 matrices and C is a 6x8 matrix which of t

If A and B are 8x3 matrices, and C is a 6x8 matrix, which of the following are defined?

a)A+C

b)CB

d)AB

f)A-B

Solution

a) Only those matrices can be added, when their order is same i.e. the number of rows and columns are same for both. Here, A is a 8x3 matrix and C is a 6x8 matrix. Therefore, A + C is not defined.

b) The matrix multiplication is defined only if he number of columns of the matrix to the left is equal to the number of rows in the matrix to the right. Here, C is a 6x8 matrix and B is a 8x3 matrix. Since the number of colums in C is the same as the number of rows in B (bvoth are equal to 8), CB is defined.

c) B^T is defined. It the matrix where the rows and the columns of B are interchanged.

d) AB is not deined as the number of columns in A is 3 while the number of rows in B is 8.

e) B is a 8x3 matrix. Therefore, B^T is a 3x8 matrix. AB^T is deined because the number of columns in A is 3 which equals the number of rows in B^T.

f) A - B is fefined because both A and B are of the same order (8x3).