Math Snap

STEP 1

1. We are multiplying two 2x2 matrices.
2. The multiplication of matrices is done by taking the dot product of rows and columns.

STEP 2

1. Calculate the element in the first row, first column.
2. Calculate the element in the first row, second column.
3. Calculate the element in the second row, first column.
4. Calculate the element in the second row, second column.

STEP 3

To find the element in the first row, first column of the resulting matrix, take the dot product of the first row of the first matrix with the first column of the second matrix:
$$(8 \times -3) + (-9 \times 4)$$ $$= -24 - 36$$ $$= -60$$

STEP 4

To find the element in the first row, second column of the resulting matrix, take the dot product of the first row of the first matrix with the second column of the second matrix:
$$(8 \times 2) + (-9 \times 7)$$ $$= 16 - 63$$ $$= -47$$

STEP 5

To find the element in the second row, first column of the resulting matrix, take the dot product of the second row of the first matrix with the first column of the second matrix:
$$(0 \times -3) + (-5 \times 4)$$ $$= 0 - 20$$ $$= -20$$

To find the element in the second row, second column of the resulting matrix, take the dot product of the second row of the first matrix with the second column of the second matrix:
$$(0 \times 2) + (-5 \times 7)$$ $$= 0 - 35$$ $$= -35$$ The resulting matrix after multiplication is:
$$\left[\begin{array}{cc} -60 & -47 \\ -20 & -35 \end{array}\right]$$