Mathematics 10 — Exercise 3.4 · Q4

Full question

Find the unknown values from the equality of the matrices.

Step-by-step solution

1. Equate the corresponding entries.

   $$x+3=7$$

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

   $$x=7-3$$

3. Simplify the constant calculation.

   $$x=4$$

4. Divide both sides by the variable coefficient.

   $$x=4\times \frac{1}{1}$$

5. Reduce the fraction.

   $$x=4$$

6. Equate the corresponding entries.

   $$y+6=4$$

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

   $$y=4-6$$

8. Simplify the constant calculation.

   $$y=-2$$

9. Divide both sides by the variable coefficient.

   $$y=-2\times \frac{1}{1}$$

10. Reduce the fraction.

    $$y=-2$$

11. Check the values in the original two matrices.

    $$(\left[\begin{array}{cc}7& -1\\ 4& -2\end{array}\right],\left[\begin{array}{cc}7& -1\\ 4& -2\end{array}\right])$$

Answer

The final answer is shown below.