To determine the sum of the given matrices:
[tex]\[ \left[\begin{array}{ccc}2 & -3 & 1 \\ -2 & 0 & 3 \\ 0 & 5 & -1\end{array}\right] \][/tex]
and
[tex]\[ \left[\begin{array}{cc}-2 & 0 \\ 3 & 1 \\ -4 & 4\end{array}\right], \][/tex]
we first need to verify if matrix addition is possible. Matrix addition is defined only for matrices of the same dimension.
1. Examining the dimensions of the matrices:
- The first matrix has dimensions [tex]\(3 \times 3\)[/tex] because it has 3 rows and 3 columns.
- The second matrix has dimensions [tex]\(3 \times 2\)[/tex] because it has 3 rows and 2 columns.
2. Compare the dimensions:
- The first matrix is [tex]\(3 \times 3\)[/tex].
- The second matrix is [tex]\(3 \times 2\)[/tex].
Since the dimensions of the two matrices are different, they cannot be added together.
Therefore, the correct answer is:
D. These two matrices cannot be added.
