Q39. - Algebra 2

Question

Solve for x if $\det \left[\begin{array}{cc}2& x\\ 5& -3\end{array}\right]=24$.

Step-by-Step Solution

Answer

The value of $x=-6$.

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

 

$\begin{array}{c}\det \left[\begin{array}{cc}2& x\\ 5& -3\end{array}\right]=24\\ 2\times \left(-3\right)-5\left(x\right)=24\end{array}$

Step 3 - Simplify for x

To further simplify multiply the values first and then find the difference.

 

 $\begin{array}{c}2\times \left(-3\right)-5\left(x\right)=24\\ -6-5x=24\\ -6-5x+6=24+6\\ -5x=20\\ x=-6\end{array}$

 

Therefore, $x=-6$.