Mathematics 10 — Exercise 3.5 · Q1 (ii)

Full question

Evaluate the determinant of the following matrix.

Step-by-step solution

1. For a 2 × 2 determinant, multiply the main diagonal and subtract the other diagonal product.

   $$D=--35-8\times \left(-3\right)$$

2. Calculate the first diagonal product.

   $$\left(-5\right)\times \left(-7\right)=35$$

3. Calculate the second diagonal product.

   $$8\times \left(-3\right)=-24$$

4. Subtract the second product, including its sign.

   $$D=35+24$$

5. Simplify the subtraction.

   $$D=59$$

Answer

The final answer is shown below.