Mathematics 10 — Exercise 3.1 · Q4

Full question

Find the unknown values from the equality of the matrices.

Step-by-step solution

1. Equate the corresponding entries.

   $$a+2=5$$

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

   $$a=5-2$$

3. Simplify the constant calculation.

   $$a=3$$

4. Divide both sides by the variable coefficient.

   $$a=3\times \frac{1}{1}$$

5. Reduce the fraction.

   $$a=3$$

6. Equate the corresponding entries.

   $$c-3=8$$

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

   $$c=8+3$$

8. Simplify the constant calculation.

   $$c=11$$

9. Divide both sides by the variable coefficient.

   $$c=11\times \frac{1}{1}$$

10. Reduce the fraction.

    $$c=11$$

11. Equate the corresponding entries.

    $$b-1=6$$

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

    $$b=6+1$$

13. Simplify the constant calculation.

    $$b=7$$

14. Divide both sides by the variable coefficient.

    $$b=7\times \frac{1}{1}$$

15. Reduce the fraction.

    $$b=7$$

16. Equate the corresponding entries.

    $$d+4=4$$

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

    $$d=4-4$$

18. Simplify the constant calculation.

    $$d=0$$

19. Divide both sides by the variable coefficient.

    $$d=0\times \frac{1}{1}$$

20. Reduce the fraction.

    $$d=0$$

21. Check the values in the original two matrices.

    $$(\left[\begin{array}{cc}5& 8\\ 6& 4\end{array}\right],\left[\begin{array}{cc}5& 8\\ 6& 4\end{array}\right])$$

Answer

The final answer is shown below.