Solve {ccc}{3}&{-2}&{0}{2}&{1}&{-2}{3}&{-1}&{1}-{ccc}{4}&{3}&{2}{4}&{2}&{-2}{1}&{3}&{-4}

$$\left( \begin{array} { c c c } { 3 } & { - 2 } & { 0 } \\ { 2 } & { 1 } & { - 2 } \\ { 3 } & { - 1 } & { 1 } \end{array} \right) - \left( \begin{array} { c c c } { 4 } & { 3 } & { 2 } \\ { 4 } & { 2 } & { - 2 } \\ { 1 } & { 3 } & { - 4 } \end{array} \right)$$

Evaluate

$$\left(\begin{matrix}-1&-5&-2\\-2&-1&0\\2&-4&5\end{matrix}\right)$$

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.

$$\left(\begin{matrix}3&-2&0\\2&1&-2\\3&-1&1\end{matrix}\right)-\left(\begin{matrix}4&3&2\\4&2&-2\\1&3&-4\end{matrix}\right)$$

To subtract two matrices, subtract the corresponding elements.

$$\left(\begin{matrix}3-4&-2-3&-2\\2-4&1-2&-2-\left(-2\right)\\3-1&-1-3&1-\left(-4\right)\end{matrix}\right)$$

Take the difference of each element of the matrix.

$$\left(\begin{matrix}-1&-5&-2\\-2&-1&0\\2&-4&5\end{matrix}\right)$$

Calculate Determinant

$$-65$$