Avaluate \( \left(\begin{array}{cc}3 & -2 \\ -7 & 5\end{array}\right)+2\left(\begin{array}{cc}-2 & 4 \\ 3 & -1\end{array}\right) \)

First, let's calculate \( 2\left(\begin{array}{cc}-2 & 4 \\ 3 & -1\end{array}\right) \): \[ 2\left(\begin{array}{cc}-2 & 4 \\ 3 & -1\end{array}\right) = \begin{array}{cc} 2 \cdot -2 & 2 \cdot 4 \\ 2 \cdot 3 & 2 \cdot -1 \end{array} = \begin{array}{cc} -4 & 8 \\ 6 & -2 \end{array} \] Now, we will add this result to \( \left(\begin{array}{cc}3 & -2 \\ -7 & 5\end{array}\right) \): \[ \left(\begin{array}{cc}3 & -2 \\ -7 & 5\end{array}\right) + \begin{array}{cc} -4 & 8 \\ 6 & -2 \end{array} = \begin{array}{cc} 3 + (-4) & -2 + 8 \\ -7 + 6 & 5 + (-2) \end{array} \] Calculating each element: 1. \( 3 - 4 = -1 \) 2. \( -2 + 8 = 6 \) 3. \( -7 + 6 = -1 \) 4. \( 5 - 2 = 3 \) Putting it all together, we get: \[ \begin{array}{cc} -1 & 6 \\ -1 & 3 \end{array} \] So, the final evaluated matrix is \[ \left(\begin{array}{cc} -1 & 6 \\ -1 & 3 \end{array}\right) \]