Solve {|c|c|}hline22.5-27.5&{38}hline27.5-32.5&{25}

$$\left. \begin{array} { | c | c | } \hline 22.5 - 27.5 & { 38 } \\ \hline 27.5 - 32.5 & { 25 } \end{array} \right.$$

Calculate Determinant

$$65$$

Steps Using Diagonal Rule

Subtract 27.5 from 22.5 to get -5.

$$det(\left(\begin{matrix}-5&38\\27.5-32.5&25\end{matrix}\right))$$

Subtract 32.5 from 27.5 to get -5.

$$det(\left(\begin{matrix}-5&38\\-5&25\end{matrix}\right))$$

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

$$-5\times 25-38\left(-5\right)$$

Multiply -5 times 25.

$$-125-38\left(-5\right)$$

Multiply 38 times -5.

$$-125-\left(-190\right)$$

Subtract -190 from -125.

$$65$$

Evaluate

$$\left(\begin{matrix}-5&38\\-5&25\end{matrix}\right)$$