iran-konkur 2018 Q138

iran-konkur · Other · konkur-riazi_1397_specialized Matrices Matrix Entry and Coefficient Identities
138- If $A = \begin{bmatrix} 1 & 3 & 6 & 24 \\ \frac{1}{2} & 1 & 2 & 8 \end{bmatrix}$, $B = \begin{bmatrix} \frac{1}{6} & \frac{1}{2} & 1 & 4 \\ \frac{1}{24} & \frac{1}{8} & \frac{1}{4} & 1 \end{bmatrix}$, and $C = \begin{bmatrix} A \\ B \end{bmatrix}$, the sum of the main diagonal entries of matrix $C^T$ is which of the following?
(1) $16$ (2) $18$ (3) $20$ (4) $24$
\textbf{138-} If $A = \begin{bmatrix} 1 & 3 & 6 & 24 \\ \frac{1}{2} & 1 & 2 & 8 \end{bmatrix}$, $B = \begin{bmatrix} \frac{1}{6} & \frac{1}{2} & 1 & 4 \\ \frac{1}{24} & \frac{1}{8} & \frac{1}{4} & 1 \end{bmatrix}$, and $C = \begin{bmatrix} A \\ B \end{bmatrix}$, the sum of the main diagonal entries of matrix $C^T$ is which of the following?

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(1) $16$ \hfill (2) $18$ \hfill (3) $20$ \hfill (4) $24$

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