Question

Evaluate the determinant

(a)$\left[\begin{array}{cc}5& -3\\ 2& -4\end{array}\right]$(b)$\left[\begin{array}{cc}-4& -6\\ 0& 7\end{array}\right]$

Short answer

Part (a) The value of the determinant is -14.

Part (b) The value of the determinant is -28.

Step-by-step solution

Part (a). Step 1. Given information

The given determinant is$\left[\begin{array}{cc}5& -3\\ 2& -4\end{array}\right]$.

Part (a) Step 2. Calculation.

Firstly write the determinant

$\left[\begin{array}{cc}5& -3\\ 2& -4\end{array}\right]$

Subtract the products of the diagonals

localid="1658971311759" $$\begin{gathered} =(5\times -4)-(-3\times 2) \\ =-20-(-6) \\ =-14 \end{gathered}$$

Hence the determinant value is -14.

Part (b) Step 1.Given information.

The given determinant is$\left[\begin{array}{cc}-4& -6\\ 0& 7\end{array}\right]$

Part (b)  Step 2. Calculation

Firstly write the determinant.

$\left[\begin{array}{cc}-4& -6\\ 0& 7\end{array}\right]$

Subtract the products of the diagonals.

$$\begin{gathered} =(7\times -4)-(0\times -6) \\ =-28+0 \\ =-28 \end{gathered}$$

Hence the determinant value is -28.