Q 4.90 - Intermediate Algebra

Question

Evaluate the determinant 

(a)

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

Step-by-Step Solution

Answer

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

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

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,

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

Hence the determinant value is -15.