Mathematics 10 — Exercise 3.1 · Q6

Full question

Find the unknown values from the equality of the matrices.

Step-by-step solution

1. Equate the corresponding entries.

   $$2\times d-1=5$$

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

   $$2\times d=5+1$$

3. Simplify the constant calculation.

   $$2\times d=6$$

4. Divide both sides by the variable coefficient.

   $$d=\frac{6}{2}$$

5. Reduce the fraction.

   $$d=3$$

6. Equate the corresponding entries.

   $$3\times b+2=11$$

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

   $$3\times b=11-2$$

8. Simplify the constant calculation.

   $$3\times b=9$$

9. Divide both sides by the variable coefficient.

   $$b=\frac{9}{3}$$

10. Reduce the fraction.

    $$b=3$$

11. Equate the corresponding entries.

    $$4=c$$

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

    $$-c=0-4$$

13. Simplify the constant calculation.

    $$-c=-4$$

14. Divide both sides by the variable coefficient.

    $$c=-\frac{4}{-1}$$

15. Reduce the fraction.

    $$c=4$$

16. Equate the corresponding entries.

    $$a+3=10$$

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

    $$a=10-3$$

18. Simplify the constant calculation.

    $$a=7$$

19. Divide both sides by the variable coefficient.

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

20. Reduce the fraction.

    $$a=7$$

21. Check the values in the original two matrices.

    $$(\left[\begin{array}{cc}10& 5\\ 11& 4\end{array}\right],\left[\begin{array}{cc}10& 5\\ 11& 4\end{array}\right])$$

Answer

The final answer is shown below.