Mathematics 10 — Exercise 3.5 · Q3

Full question

Find x so the matrix is singular.

Step-by-step solution

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

   $$D=15\times x-6\times 5$$

2. Calculate the first diagonal product.

   $$15\times x=15\times x$$

3. Calculate the second diagonal product.

   $$6\times 5=30$$

4. Subtract the second product, including its sign.

   $$D=15\times x-30$$

5. Simplify the subtraction.

   $$D=15\times x-30$$

6. For a singular matrix set its determinant equal to zero.

   $$15\times x-30=0$$

7. Equate the corresponding entries.

   $$15\times x-30=0$$

8. Collect the variable terms on the left and constants on the right.

   $$15\times x=0+30$$

9. Simplify the constant calculation.

   $$15\times x=30$$

10. Divide both sides by the variable coefficient.

    $$x=\frac{30}{15}$$

11. Reduce the fraction.

    $$x=2$$

Answer

The final answer is shown below.