Answer :
To determine the sum of two matrices, we need to ensure that their dimensions are the same. A matrix's dimension is described by the number of rows and columns it has.
Let's examine the dimensions of the given matrices:
The first matrix is:
[tex]\[ \left[\begin{array}{ccc} 2 & -3 & 1 \\ -2 & 0 & 3 \\ 0 & 5 & -1 \end{array}\right] \][/tex]
This matrix has 3 rows and 3 columns, so its dimensions are \(3 \times 3\).
The second matrix is:
[tex]\[ \left[\begin{array}{cc} -2 & 0 \\ 3 & 1 \\ -4 & 4 \end{array}\right] \][/tex]
This matrix has 3 rows and 2 columns, so its dimensions are \(3 \times 2\).
To add two matrices, they must have the same dimensions. Since the first matrix is \(3 \times 3\) and the second matrix is \(3 \times 2\), their dimensions do not match. Therefore, they cannot be added together.
The correct answer is:
D. These two matrices cannot be added.
Let's examine the dimensions of the given matrices:
The first matrix is:
[tex]\[ \left[\begin{array}{ccc} 2 & -3 & 1 \\ -2 & 0 & 3 \\ 0 & 5 & -1 \end{array}\right] \][/tex]
This matrix has 3 rows and 3 columns, so its dimensions are \(3 \times 3\).
The second matrix is:
[tex]\[ \left[\begin{array}{cc} -2 & 0 \\ 3 & 1 \\ -4 & 4 \end{array}\right] \][/tex]
This matrix has 3 rows and 2 columns, so its dimensions are \(3 \times 2\).
To add two matrices, they must have the same dimensions. Since the first matrix is \(3 \times 3\) and the second matrix is \(3 \times 2\), their dimensions do not match. Therefore, they cannot be added together.
The correct answer is:
D. These two matrices cannot be added.
