Find 7A. If \( A=\left[\begin{array}{ccc}1 & 0 & 3 \\ 2 & -1 & 2 \\ 0 & 2 & 1\end{array}\right] \)
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To find \( 7A \), you simply multiply each element of the matrix \( A \) by 7. Given \( A = \left[\begin{array}{ccc}1 & 0 & 3 \\ 2 & -1 & 2 \\ 0 & 2 & 1\end{array}\right] \), we perform the multiplication: \[ 7A = 7 \cdot \left[\begin{array}{ccc} 1 & 0 & 3 \\ 2 & -1 & 2 \\ 0 & 2 & 1 \end{array}\right] = \left[\begin{array}{ccc} 7 \cdot 1 & 7 \cdot 0 & 7 \cdot 3 \\ 7 \cdot 2 & 7 \cdot -1 & 7 \cdot 2 \\ 7 \cdot 0 & 7 \cdot 2 & 7 \cdot 1 \end{array}\right] \] Calculating each element: \[ = \left[\begin{array}{ccc} 7 & 0 & 21 \\ 14 & -7 & 14 \\ 0 & 14 & 7 \end{array}\right] \] Thus, the result is: \[ 7A = \left[\begin{array}{ccc} 7 & 0 & 21 \\ 14 & -7 & 14 \\ 0 & 14 & 7 \end{array}\right] \]
