Question

The value of the determinant $\begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}$ is:

• A. 10
• B. -2
• C. 2
• D. 0

Hint:

Think of it as "Main diagonal product minus the off-diagonal product." Always be careful with negative signs if the numbers inside are negative!

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
For a $2 \times 2$ matrix $\begin{vmatrix} a & b \\ c & d \end{vmatrix}$, the determinant is calculated using the formula: $(a \times d) - (b \times c)$.
Step 2: Detailed Explanation:
In this determinant: $a = 1, b = 2, c = 3, d = 4$. Applying the formula: $$(1 \times 4) - (2 \times 3)$$ $$4 - 6 = -2$$
Step 3: Final Answer:
The correct option is (b).