To determine the size of the new matrix resulting from the multiplication of two matrices, we need to look at the dimensions of the matrices being multiplied.
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The first matrix: \[ \begin{bmatrix} -4 & 0 \ 2 & 7 \ -1 & -2 \end{bmatrix} \] This matrix has 3 rows and 2 columns, so its dimensions are \(3 \times 2\).
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The second matrix: \[ \begin{bmatrix} 5 & -3 & 4 \ 2 & 7 & -1 \ -5 & 9 & 0 \end{bmatrix} \] This matrix has 3 rows and 3 columns, so its dimensions are \(3 \times 3\).
In 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 2 columns and the second matrix has 3 rows, so multiplication is not possible.
Therefore, the multiplication of these two matrices cannot be performed, and we cannot determine the size of a resulting matrix because a product does not exist.