Mathematics 10 — Exercise 3.5 · Q2 A

Full question

Determine whether the following matrix is singular or non-singular by evaluating its determinant.

Step-by-step solution

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

   $$D=5\times 2-3\times 3$$

2. Calculate the first diagonal product.

   $$5\times 2=10$$

3. Calculate the second diagonal product.

   $$3\times 3=9$$

4. Subtract the second product, including its sign.

   $$D=10-9$$

5. Simplify the subtraction.

   $$D=1$$

6. A zero determinant means singular; a nonzero determinant means non-singular.

Answer

Non-singular