Question

Given the following:
A = 3 * 3
B = 2 * 4
C = 4 * 3
D = 3 * 2

Which of the following are defined:
A * D
D * B
A * D^T
C * D + A * D^T
A * B
A * D^T + C

Answer 1

Answer on Question #51652 – Math – Matrix | Tensor Analysis

Question

Given the following:

A = 3 * 3

B = 2 * 4

C = 4 * 3

D = 3 * 2

Which of the following are defined:

1) A * D;

2) D * B;

3) A * D^T;

4) C * D + A * D^T;

5) A * B;

6) A * D^T + C?

Solution

The product AB is defined only if the number of columns in A and that of B are equal.

1) A * D. Matrix A has 3 columns, D has 3 rows. Therefore, A * D is defined.

2) D * B. Matrix D has 2 columns, B has 2 rows. Therefore, D * B is defined.

3) A * D^T. Matrix A has 3 columns, D has 3 rows and 2 columns, then D^T has 2 rows. Therefore, A * D^T is not defined.

4) C * D + A * D^T. Matrix C has 3 columns, D has 3 rows, A has 3 columns, D^T has 2 rows. Therefore, C * D + A * D^T is not defined.

5) A * B. Matrix A has 3 columns, B has 2 rows. Therefore, A * B is not defined.

6) A * D^T + C. Matrix A has 3 columns, D^T has 2 rows. Therefore, A * D^T + C is not defined.

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