Marphua 2(} 1&-2 -3&-7 paBHa B sibepute oAMH OTBer: (} 11&0 0&-28 ) (} 10&-1 2&-18 ) (} 10&-1 0&28 ) (} 11&1 0&-28 ) (} 11&-1 -12&-28 ) C

To solve the given matrix expression, we need to perform scalar multiplication and matrix addition.<br /><br />Given expression: $2(\begin{matrix} 1&-2\\ -3&-7\end{matrix} )+3(\begin{matrix} 3&-2\\ 1&-4\end{matrix} )^{T}$<br /><br />Step 1: Perform scalar multiplication on the first matrix.<br />$2(\begin{matrix} 1&-2\\ -3&-7\end{matrix} ) = (\begin{matrix} 2&-4\\ -6&-14\end{matrix} )$<br /><br />Step 2: Transpose the second matrix.<br />$(\begin{matrix} 3&-2\\ 1&-4\end{matrix} )^{T} = (\begin{matrix} 3&1\\ -2&-4\end{matrix} )$<br /><br />Step 3: Perform scalar multiplication on the transposed matrix.<br />$3(\begin{matrix} 3&1\\ -2&-4\end{matrix} ) = (\begin{matrix} 9&3\\ -6&-12\end{matrix} )$<br /><br />Step 4: Add the two resulting matrices.<br />$(\begin{matrix} 2&-4\\ -6&-14\end{matrix} ) + (\begin{matrix} 9&3\\ -6&-12\end{matrix} ) = (\begin{matrix} 11&-1\\ -12&-28\end{matrix} )$<br /><br />Therefore, the correct answer is:<br />$(\begin{matrix} 11&-1\\ -12&-28\end{matrix} )$