Solve the equation for x.
-$$\left| \begin{array} { l l }
3 & x \
x & 4
\end{array} \right| = - 4$$
A) $\{ 16 \}$
B) $\{ - 4,4 \}$
C) $\left\{ \frac { 4 } { 3 } \right\}$
D) $\varnothing$

Question

Solve the equation for x.
-$$\left| \begin{array} { l l } 
3 & x \
x & 4
\end{array} \right| = - 4$$
A) $\{ 16 \}$
B) $\{ - 4,4 \}$
C) $\left\{ \frac { 4 } { 3 } \right\}$
D) $\varnothing$

Quizplus · Accepted Answer

The determinant of a 2x2 matrix is found by multiplying the elements on the diagonal and then subtracting the product of the off-diagonal elements. So, for the given matrix, the determinant is $3*4 - x*x = 12 - x^2$. Setting this equal to -4 gives the equation $12 - x^2 = -4$. Solving for $x^2$ gives $x^2 = 16$, which means $x = 4$ or $x = -4$. Therefore, the correct answer is $\{ -4, 4 \}$.

Solve the Equation for X ∣3xx4∣=−4\left| \begin{array} { l l } 3 & x \\x & 4\end{array} \right| = - 4​3x​x4​​=−4

Solve the Equation for X $\left| \begin{array} { l l } 3 & x \\x & 4\end{array} \right| = - 4$