Q.31 The determinant of the matrix
(
| 4 | -6 |
| -3 | 2 |
) is ________
Introduction
Matrices are widely used in algebra, engineering, physics, and computer applications. One of the most important concepts is the determinant.
Here we evaluate the determinant of the following 2×2 matrix:
| | | 4 | -6 | | |
| | | -3 | 2 | | |
Formula for Determinant of a 2×2 Matrix
For the matrix
| | | a | b | | |
| | | c | d | | |
The determinant is:
Determinant = ad − bc
Step-by-Step Solution
Given: a = 4, b = −6, c = −3, d = 2
Apply the formula:
Determinant = (4 × 2) − (−6 × −3)
- 4 × 2 = 8
- −6 × −3 = 18
Subtract:
Determinant = 8 − 18 = −10
Correct Answer
The determinant of the matrix is −10.
Conclusion
Using the rule ad − bc, we found the determinant of the given matrix as −10.
Because the value is not zero, the matrix is invertible.
✔ Final Answer: −10
