Question

Find the value of the following determinant:

| 4 3 |
| 2 7 |

Solution:
Determinant = (4 × 7) − (3 × 2) = 28 − 6 = 22

Final Answer: 22

Hint:

For a \(2 \times 2\) determinant, simply multiply the diagonal elements and subtract the product of the off-diagonal elements: \(ad - bc\).

Answer 1

Step 1: Recall the formula for a 2×2 determinant.
For a determinant of order 2,
| a b |
| c d |
= ad − bc

Step 2: Substitute the given values.
Here, a = 4, b = 3, c = 2, and d = 7.
Determinant = (4 × 7) − (3 × 2)

Step 3: Simplify.
Determinant = 28 − 6 = 22

Step 4: Conclusion.
Hence, the value of the given determinant is 22.

Final Answer:

22