Question

Evaluate the determinant

(a)

$\left[\begin{array}{cc}-1& 3\\ -2& 4\end{array}\right]\left(\mathrm{b}\right)\left[\begin{array}{cc}-7& -3\\ -5& 0\end{array}\right]$

Short answer

Part (a). The value of the determinant is 2.

Part (b). The value of the determinant is -15.

Step-by-step solution

Part (a) Step 1. Given information

The given determinant is $\left[\begin{array}{cc}-1& 3\\ -2& 4\end{array}\right]$

Part (a) Step 2. Calculation

Firstly write the determinant

$\left[\begin{array}{cc}-1& 3\\ -2& 4\end{array}\right]$

Subtract the products of the diagonals

$$\begin{gathered} =(-1\times 4)-(3\times -2) \\ =-4-(-6) \\ =2 \end{gathered}$$

Hence the determinant value is 2.

Part (b) Step 1. Given information.

The given determinant is $\left[\begin{array}{cc}-7& -3\\ -5& 0\end{array}\right]$

Part (b) Step 2. Calculation.

Firstly write the determinant

$\left[\begin{array}{cc}-7& -3\\ -5& 0\end{array}\right]$

Subtract the products of the diagonals,

localid="1645170808775" $$\begin{gathered} =(-7\times 0)-(-3\times -5) \\ =0-\left(15\right) \\ =-15 \end{gathered}$$

Hence the determinant value is -15.