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

Question

open square bracket,
begin matrix
row 1, column 1, minus, 2
row 1, column 2, 1
row 1, column 3, minus, 6
row 1, column 4, minus, 8
row 1, column 5, minus, 2
row 2, column 1, 9
row 2, column 2, 2
row 2, column 3, 7
row 2, column 4, 4
row 2, column 5, minus, 5
row 3, column 1, minus, 8
row 3, column 2, 9
row 3, column 3, minus, 6
row 3, column 4, minus, 6
row 3, column 5, minus, 3
row 4, column 1, 3
row 4, column 2, minus, 8
row 4, column 3, 6
row 4, column 4, minus, 1
row 4, column 5, 9
row 5, column 1, minus, 2
row 5, column 2, 9
row 5, column 3, minus, 2
row 5, column 4, 4
row 5, column 5, 9
end matrix
, close square bracket, plus, open square bracket,
begin matrix
row 1, column 1, minus, 7
row 1, column 2, minus, 1
row 1, column 3, 0
row 1, column 4, 7
row 1, column 5, minus, 1
row 1, column 6, 6
row 2, column 1, minus, 7
row 2, column 2, 8
row 2, column 3, 2
row 2, column 4, minus, 8
row 2, column 5, 5
row 2, column 6, 4
row 3, column 1, 5
row 3, column 2, 7
row 3, column 3, 6
row 3, column 4, 8
row 3, column 5, minus, 7
row 3, column 6, minus, 7
row 4, column 1, minus, 1
row 4, column 2, minus, 1
row 4, column 3, minus, 7
row 4, column 4, minus, 8
row 4, column 5, minus, 8
row 4, column 6, 3
row 5, column 1, minus, 4
row 5, column 2, minus, 7
row 5, column 3, minus, 7
row 5, column 4, 2
row 5, column 5, 6
row 5, column 6, minus, 9
end matrix
, close square bracket
​

−2
9
−8
3
−2
​

1
2
9
−8
9
​

−6
7
−6
6
−2
​

−8
4
−6
−1
4
​

−2
−5
−3
9
9
​

​
+
​

−7
−7
5
−1
−4
​

−1
8
7
−1
−7
​

0
2
6
−7
−7
​

7
−8
8
−8
2
​

−1
5
−7
−8
6
​

6
4
−7
3
−9
​

​

Answer
Attempt 1 out of 2

The result of the operation is

Answer 1

To determine whether the operation of addition on the two matrices is defined and to find the order of the resulting matrix, we first need to identify the dimensions of the given matrices.

Matrix A:

The first matrix is defined as follows:

\[ \begin{bmatrix} -2 & 1 & -6 & -8 & -2 \ 9 & 2 & 7 & 4 & -5 \ -8 & 9 & -6 & -6 & -3 \ 3 & -8 & 6 & -1 & 9 \ -2 & 9 & -2 & 4 & 9 \end{bmatrix} \]

This matrix has 5 rows and 5 columns, so its order is 5 x 5.

Matrix B:

The second matrix is defined as follows:

\[ \begin{bmatrix} -7 & -1 & 0 & 7 & -1 & 6 \ -7 & 8 & 2 & -8 & 5 & 4 \ 5 & 7 & 6 & 8 & -7 & -7 \ -1 & -1 & -7 & -8 & -8 & 3 \ -4 & -7 & -7 & 2 & 6 & -9 \end{bmatrix} \]

This matrix has 5 rows and 6 columns, so its order is 5 x 6.

Addition Operation:

The operation of matrix addition is defined only when both matrices have the same dimensions. In this case, Matrix A is 5 x 5 and Matrix B is 5 x 6. Since the number of columns is different (5 columns for Matrix A and 6 columns for Matrix B), the addition operation is not defined.

Conclusion:

The operation of adding the two matrices is not defined due to differing dimensions. Therefore, we cannot determine an order for a resulting matrix since the addition cannot be performed.