Solve {cc}{3}&{4}{-1}&{-2^11}

$$\left( \begin{array} { c c } { 3 } & { 4 } \\ { - 1 } & { - 2 ^ { 11 } } \end{array} \right)$$

Calculate Determinant

$$-6140$$

Steps Using Diagonal Rule

Calculate 2 to the power of 11 and get 2048.

$$det(\left(\begin{matrix}3&4\\-1&-2048\end{matrix}\right))$$

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

$$3\left(-2048\right)-4\left(-1\right)$$

Multiply 3 times -2048.

$$-6144-4\left(-1\right)$$

Multiply 4 times -1.

$$-6144-\left(-4\right)$$

Subtract -4 from -6144.

$$-6140$$

Evaluate

$$\left(\begin{matrix}3&4\\-1&-2048\end{matrix}\right)$$