Determine if the following operation on the two given matrices is defined, and if it is, determine the order of the resulting matrix.

Question

-2 -6 | -4 8 8
-8 5| -6 6 -8
-3 -3 0

It is defined and the order of the resulting matrix is 2x2.
It is defined and the order of the resulting matrix is 2x2.

It is defined and the order of the resulting matrix is 2x3.
It is defined and the order of the resulting matrix is 2x3.

This is undefined.
This is undefined.

It is defined and the order of the resulting matrix is a 2x3.

Answer 1

To determine if the operation on the two given matrices is defined, we need to know the dimensions (order) of each matrix.

The first matrix: \[ \begin{bmatrix} -2 & -6 \ -8 & 5 \end{bmatrix} \] is a 2x2 matrix (2 rows and 2 columns).

The second matrix: \[ \begin{bmatrix} -4 & 8 & 8 \ -6 & 6 & -8 \ -3 & -3 & 0 \end{bmatrix} \] is a 3x3 matrix (3 rows and 3 columns).

The operation between two matrices (like addition or multiplication) is defined under specific conditions:

• For matrix addition or subtraction, both matrices must have the same dimensions.
• For matrix multiplication, the number of columns in the first matrix must equal the number of rows in the second matrix.

In this case, the first matrix has order 2x2 and the second matrix has order 3x3. Since their dimensions do not match, the addition or subtraction is undefined for the two matrices.

Therefore, the correct assertion is: This is undefined.