Question

determinant help me ​

Answer 1

Answer:

The values of $x$ are 4 and -4.

Step-by-step explanation:

The determinant of a 2x2 matrix is,

$\left|\begin{array}{cc}a&b&\\c&d\end{array}\right| = ad-bc$

Given that,

$\left|\begin{array}{cc}x+3&2&\\3&x-3\end{array}\right|=1$

So using the formula, we obtain a quadratic equation in the variable $x$ .

$\implies (x+3)(x-3)-2\times 3= 1\\\\\implies x^2-9-6 =1\\\\\implies x^2-15=1\\\\\implies x^2=15+1=16\\\\\implies x=4\ \ \ or \ \ -4$

The two possible values of $x$ are 4 and -4.