Q2. - Algebra 2

Question

Khalid and Erica are finding the determinant of $\left[\begin{array}{cc}8& 3\\ -5& 2\end{array}\right]$.

Who is correct? Explain your reasoning.

Step-by-Step Solution

Answer

Khalid’s answer is correct and Erica’s answers is wrong because Erica did not subtract the products of two diagonals rather, she did the opposite as she added the product of two diagonals.

Step 1 - Define the determinant of second-order matrix

The determinant of second order matrix is found by calculating the difference of the product of the two diagonals, that is., $\left|\begin{array}{cc}a& b\\ c& d\end{array}\right|=ad-bc$ .

Step 2 - Find the determinant

Apply the definition of the method of finding determinant of second order

matrix $\left|\begin{array}{cc}8& 3\\ -5& 2\end{array}\right|$.

$\begin{array}{c}\left|\begin{array}{cc}8& 3\\ -5& 2\end{array}\right|=8\times \left(2\right)-3\left(-5\right)\\ =16+15\\ =31\end{array}$

Step 3 - State the conclusion

Since Khalid’s answer is 31 and Erica’s answer is 1, therefore, Khalid’s answer is correct and Erica’s answers is wrong because Erica did not subtract the products of two diagonals rather, she did the opposite as she added the product of two diagonals.