Question

Evaluate the determinant $$\begin{gathered} \left[2-1-3 \\ 03-4 \\ 3-4-3\right] \end{gathered}$$by expanding by minors.

Short answer

The value of the determinant is -11.

Step-by-step solution

Step 1. Given information

The given determinant is

$$\begin{gathered} \left[2-1-3 \\ 03-4 \\ 3-4-3\right] \end{gathered}$$

Step 2. Calculation

Expand the determinant using second row.

Be careful with the signs

$$\begin{gathered} \left[\begin{array}{ccc}+& -& +\\ -& +& -\\ +& -& +\end{array}\right] \\ -0\left[\begin{array}{cc}3& -4\\ -4& -3\end{array}\right]+3\left[\begin{array}{cc}2& -3\\ 3& -3\end{array}\right]-(-4)\left[\begin{array}{cc}2& -1\\ 3& -4\end{array}\right] \\ =0+3(-6+9)+4(-8+3) \\ =3\left(3\right)+4(-5) \\ =9-20 \\ =-11 \end{gathered}$$