Q 4.89 - Intermediate Algebra

Question

Evaluate the determinant

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

Step-by-Step Solution

Answer

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

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

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

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

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.