QuestionJuly 15, 2025

Perform the indicated matrix operation, if possible. [} -2x+2y&-5x+y 7x-4y&5x-5y ] Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. The resulting matrix is square . (Simplify your answer.) B. The matrices cannot be added.

Perform the indicated matrix operation, if possible. [} -2x+2y&-5x+y 7x-4y&5x-5y ] Select the correct choice below and, if necessary,fill in the answer box to complete your choice. A. The resulting matrix is square . (Simplify your answer.) B. The matrices cannot be added.
Perform the indicated matrix operation, if possible.
[} -2x+2y&-5x+y 7x-4y&5x-5y ]
Select the correct choice below and, if necessary,fill in the answer box to complete your choice.
A. The resulting matrix is square  . (Simplify your answer.)
B. The matrices cannot be added.

Solution
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Answer

\begin{bmatrix} -10x + 11y & -3x + y \\ x & 11x - y \end{bmatrix} Explanation 1. Check Matrix Dimensions Both matrices are 2 \times 2, so they can be added. 2. Add Corresponding Elements Add each corresponding element from the two matrices: - First row, first column: (-2x + 2y) + (-8x + 9y) = -10x + 11y - First row, second column: (-5x + y) + (2x) = -3x + y - Second row, first column: (7x - 4y) + (4y - 6x) = x - Second row, second column: (5x - 5y) + (6x + 4y) = 11x - y

Explanation

1. Check Matrix Dimensions<br /> Both matrices are $2 \times 2$, so they can be added.<br /><br />2. Add Corresponding Elements<br /> Add each corresponding element from the two matrices:<br /><br />- First row, first column: $(-2x + 2y) + (-8x + 9y) = -10x + 11y$<br />- First row, second column: $(-5x + y) + (2x) = -3x + y$<br />- Second row, first column: $(7x - 4y) + (4y - 6x) = x$<br />- Second row, second column: $(5x - 5y) + (6x + 4y) = 11x - y$
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