Solve {cc}{-15/2}&{-15}{3}&{1}

$$\left| \begin{array} { c c } { - \frac { 15 } { 2 } } & { - 15 } \\ { 3 } & { 1 } \end{array} \right|$$

Evaluate

$$\frac{75}{2}=37.5$$

Steps Using Diagonal Rule

Find the determinant of the matrix.

$$det(\left(\begin{matrix}-\frac{15}{2}&-15\\3&1\end{matrix}\right))$$

For the 2\times 2 matrix \left(\begin{matrix}a&b\\c&d\end{matrix}\right), the determinant is ad-bc.

$$-\frac{15}{2}-\left(-15\times 3\right)$$

Multiply -15 times 3.

$$-\frac{15}{2}-\left(-45\right)$$

Subtract -45 from -\frac{15}{2}.

$$\frac{75}{2}$$

Factor

$$\frac{3 \cdot 5 ^ {2}}{2} = 37\frac{1}{2} = 37.5$$