Question

The order of the matrix B is 4 × 5, the order of the matrix D is 4 × 2 and the size of the matrix E is 5 × 4; then the order of the matrix (B^T × D) + ED is: (note that: T stands for transpose)

Answer 1

so the order will be 5 x 2

Explanation:

When we find the transpose of a matrix we change the rows into columns and columns into rows so the order is also reversed.

The order of B transpose will be reversed i.e. it will 5 x 4.

When we multiply two matrices we check the columns of the first matrix should be equal to the rows of the second matrix and the answer should contain the rows of the first matrix and the columns of the second matrix as the order of the resultant matrix

B^T (5 X 4) X D ( 4 X 2)

B^TD (5 X 2)

Now ED will be

E (5 x 4) D (4 x 2)

ED ( 5 x 2)

Now adding

B^TD (5 X 2) + ED ( 5 x 2) = (B^T × D) + ED ( 5 x 2)

In addition the order does not change.