Solve {ccc}{-5}&{-13}&{15}{-13}&{74}&{-82}{-21}&{-82}&{31}-{lll}{2}&{0}&{0}{0}&{2}&{0}{0}&{0}&{2}

$$\left( \begin{array} { c c c } { - 5 } & { - 13 } & { 15 } \\ { - 13 } & { 74 } & { - 82 } \\ { - 21 } & { - 82 } & { 31 } \end{array} \right) - \left( \begin{array} { l l l } { 2 } & { 0 } & { 0 } \\ { 0 } & { 2 } & { 0 } \\ { 0 } & { 0 } & { 2 } \end{array} \right)$$

Evaluate

$$\left(\begin{matrix}-7&-13&15\\-13&72&-82\\-21&-82&29\end{matrix}\right)$$

Steps Using Rules for Matrix Arithmetic

You can add or subtract two matrices only if both matrices have the same number of rows and columns.

$$\left(\begin{matrix}-5&-13&15\\-13&74&-82\\-21&-82&31\end{matrix}\right)-\left(\begin{matrix}2&0&0\\0&2&0\\0&0&2\end{matrix}\right)$$

To subtract two matrices, subtract the corresponding elements.

$$\left(\begin{matrix}-5-2&-13&15\\-13&74-2&-82\\-21&-82&31-2\end{matrix}\right)$$

Take the difference of each element of the matrix.

$$\left(\begin{matrix}-7&-13&15\\-13&72&-82\\-21&-82&29\end{matrix}\right)$$

Calculate Determinant

$$43835$$