iran-konkur 2021 Q143

iran-konkur · Other · konkur-riazi_1400_specialized 3x3 Matrices Matrix Algebraic Properties and Abstract Reasoning
143. Suppose $A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & -1 & 1 \end{bmatrix} \begin{bmatrix} 7 & 8 & 4 \\ 3 & 2 & 5 \\ 6 & 9 & 3 \end{bmatrix} \begin{bmatrix} 0 & 1 & -1 \\ 1 & 0 & 0 \\ 0 & 1 & 1 \end{bmatrix}$. The sum of the entries of the third row of matrix $A$ is:
(1) $3$ (2) $5$ (3) $12$ (4) $13$
\textbf{143.} Suppose $A = \begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & 0 \\ 0 & -1 & 1 \end{bmatrix} \begin{bmatrix} 7 & 8 & 4 \\ 3 & 2 & 5 \\ 6 & 9 & 3 \end{bmatrix} \begin{bmatrix} 0 & 1 & -1 \\ 1 & 0 & 0 \\ 0 & 1 & 1 \end{bmatrix}$. The sum of the entries of the third row of matrix $A$ is:

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(1) $3$ \hfill (2) $5$ \hfill (3) $12$ \hfill (4) $13$

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