Question

The value of the determinant
\includegraphics[width=0.5\linewidth]{1.png}
is:

• A. $-2$
• B. $2$
• C. $-5$
• D. $5$

Hint:

For any $2 \times 2$ determinant, always remember the shortcut formula:
{(Top-left × Bottom-right) − (Top-right × Bottom-left)}.

Answer 1

The Correct Option is A

Step 1: Recall the formula for a $2 \times 2$ determinant.
For a matrix \[ \begin{vmatrix} a & b
c & d \end{vmatrix}, \] the determinant is calculated using the formula: \[ ad - bc \]
Step 2: Identify the matrix elements.
From the given matrix:
\[ a = 1,\quad b = 2,\quad c = 3,\quad d = 4 \]
Step 3: Substitute the values into the formula.
\[ \text{Determinant} = (1 \times 4) - (2 \times 3) \]
Step 4: Perform the calculations.
\[ = 4 - 6 \]
\[ = -2 \]
Step 5: Conclusion.
The value of the given determinant is $-2$.