Question

Solve: \[ \begin{vmatrix} x & 1\\ 2 & x \end{vmatrix}=0 \]

• A. \(x=\pm\sqrt{2}\)
• B. \(x=\pm1\)
• C. \(x=\pm2\)
• D. \(x=0\)

Hint:

For determinant: \[ \begin{vmatrix} a & b c & d \end{vmatrix} \] always use: \[ ad-bc \]

Answer 1

The Correct Option is A

Concept: For a \(2\times2\) determinant: \[ \begin{vmatrix} a & b\\ c & d \end{vmatrix} = ad-bc \]

Step 1: Expanding determinant. \[ \begin{vmatrix} x & 1\\ 2 & x \end{vmatrix} = x(x)-(1)(2) \] \[ =x^2-2 \] Given determinant equals zero: \[ x^2-2=0 \]

Step 2: Solving equation. \[ x^2=2 \] \[ x=\pm\sqrt{2} \] Final Answer: \[ \boxed{(A)\ x=\pm\sqrt{2}} \]