Subjects linear algebra

Matrix Product Check

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Matrix Product Check


1. The problem involves matrices multiplication followed by evaluating a scalar expression. 2. The first matrix is a 3x3: $$\begin{pmatrix} -2 & 0 & 5 \\ -1 & 3 & 6 \\ 0 & 1 & -1 \end{pmatrix}$$ 3. The second matrix is a 3x2: $$\begin{pmatrix} -2 & 0 \\ -1 & 3 \\ 0 & 1 \end{pmatrix}$$ 4. Multiplying these matrices directly is undefined since their inner dimensions do not agree: the first is 3x3 and the second 3x2, so matrix multiplication $$3 \times 3 \cdot 3 \times 2$$ is valid resulting in a 3x2 matrix. 5. However, the problem seems to consider multiplication of two 2x2 determinant parts or scalar products, suggesting a conceptual confusion. 6. The shown scalar operation: $$(6 + 0 + (-5)) (0 + (-12) + 0) = 1 \times (-12) = -12$$, but you wrote $1 + 12 = 13$, which is incorrect. 7. The calculation steps for the scalar product are not correct; to find the product of determinants or scalar products, sums must be carefully computed. 8. Therefore, the final answer given as 13 is not correct. Final conclusion: The matrix size and multiplication logic or scalar product computation is misapplied resulting in an incorrect value of 13. Correct computations lead to a different result, not 13.