QuestionJuly 14, 2025

Find the following matrix product, if it exists. [} -3&-4&-5 -4&-4&-2 ] Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. [} -3&-4&-5 -4&-4&-2 ]=square =(Simplify your answer.) B. The product does not exist.

Find the following matrix product, if it exists. [} -3&-4&-5 -4&-4&-2 ] Select the correct choice and, if necessary, fill in the answer box to complete your choice. A. [} -3&-4&-5 -4&-4&-2 ]=square =(Simplify your answer.) B. The product does not exist.
Find the following matrix product, if it exists.
[} -3&-4&-5 -4&-4&-2 ]
Select the correct choice and, if necessary, fill in the answer box to complete your choice.
A. [} -3&-4&-5 -4&-4&-2 ]=square  =(Simplify your answer.)
B. The product does not exist.

Solution
4.3(340 votes)

Answer

\begin{bmatrix} 22 & 3 \\ 16 & 6 \end{bmatrix} Explanation 1. Verify Matrix Dimensions The first matrix is 2 \times 3 and the second matrix is 3 \times 2. The inner dimensions match, so the product exists and will be a 2 \times 2 matrix. 2. Calculate Element (1,1) Use **matrix multiplication**: (-3)(0) + (-4)(-3) + (-5)(-2) = 0 + 12 + 10 = 22. 3. Calculate Element (1,2) (-3)(0) + (-4)(-2) + (-5)(1) = 0 + 8 - 5 = 3. 4. Calculate Element (2,1) (-4)(0) + (-4)(-3) + (-2)(-2) = 0 + 12 + 4 = 16. 5. Calculate Element (2,2) (-4)(0) + (-4)(-2) + (-2)(1) = 0 + 8 - 2 = 6.

Explanation

1. Verify Matrix Dimensions<br /> The first matrix is $2 \times 3$ and the second matrix is $3 \times 2$. The inner dimensions match, so the product exists and will be a $2 \times 2$ matrix.<br /><br />2. Calculate Element (1,1)<br /> Use **matrix multiplication**: $(-3)(0) + (-4)(-3) + (-5)(-2) = 0 + 12 + 10 = 22$.<br /><br />3. Calculate Element (1,2)<br /> $(-3)(0) + (-4)(-2) + (-5)(1) = 0 + 8 - 5 = 3$.<br /><br />4. Calculate Element (2,1)<br /> $(-4)(0) + (-4)(-3) + (-2)(-2) = 0 + 12 + 4 = 16$.<br /><br />5. Calculate Element (2,2)<br /> $(-4)(0) + (-4)(-2) + (-2)(1) = 0 + 8 - 2 = 6$.
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