Question

What is the value of the determinant \(\begin{vmatrix} 1 & 2 1 & 3 \end{vmatrix}\)?

• A. 1/3
• B. 4/3
• C. 2/3
• D. 1

Hint:

2x2 determinant: \(ad - bc\).
3x3 determinant: Expansion by minors.
Determinants are used in solving linear equations and matrix algebra.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question tests knowledge of determinant calculation for a 2x2 matrix.

Step 2: Key Formula or Approach:
For a 2x2 determinant \(\begin{vmatrix} a & b c & d \end{vmatrix}\), the value is \(ad - bc\).

Step 3: Detailed Explanation:
Given determinant: \(\begin{vmatrix} 1 & 2 1 & 3 \end{vmatrix}\)
Using the formula:
\(= (1 \times 3) - (2 \times 1)\)
\(= 3 - 2 = 1\)
Thus, the value of the determinant is 1.

Step 4: Final Answer:
Thus, the value of the determinant is 1.
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