If $\left|\begin{array}{cc}2 & 3-x \

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Target Exam

CUET

Subject

-- Mathematics - Section A

Chapter

Determinants

Question:

If $\left|\begin{array}{cc}2 & 3-x \\ x & 1\end{array}\right|=0$, then the values of x are:

Options:

1 and 3

1 and 2

2 and 3

3 and 0

Correct Answer:

1 and 2

Explanation:

$\left|\begin{array}{cc}2 & 3-x \\ x & 1\end{array}\right|=0$

⇒ 2 × 1 - (3 - x)(x)

⇒ 2 - 3x + x² = 0

⇒ x² - 3x + 2 = 0

⇒ x² - 2x - x + 2 = 0

⇒ x(x - 2) - 1(x - 2) = 0

⇒ (x - 1) (x - 2) = 0

⇒ x = 1, 2