Mathematics 10 — Exercise 3.4 · Q1 (v) BA

Full question

Find BA, if possible.

Step-by-step solution

1. 2 columns in the first matrix match 2 rows in the second. The product has 3 rows and 3 columns.

   $$(\left[\begin{array}{cc}1& 5\\ 2& 4\\ 1& 6\end{array}\right],\left[\begin{array}{ccc}1& 2& 2\\ 3& 1& 1\end{array}\right])$$

2. Entry (1,1): pair row 1 with column 1 and add their products.

   $$1\times 1+5\times 3$$

3. Calculate this individual product, including its signs.

   $$1\times 1=1$$

4. Calculate this individual product, including its signs.

   $$5\times 3=15$$

5. Add the calculated products to obtain this entry.

   $$1+15=16$$

6. Entry (1,2): pair row 1 with column 2 and add their products.

   $$1\times 2+5\times 1$$

7. Calculate this individual product, including its signs.

   $$1\times 2=2$$

8. Calculate this individual product, including its signs.

   $$5\times 1=5$$

9. Add the calculated products to obtain this entry.

   $$2+5=7$$

10. Entry (1,3): pair row 1 with column 3 and add their products.

    $$1\times 2+5\times 1$$

11. Calculate this individual product, including its signs.

    $$1\times 2=2$$

12. Calculate this individual product, including its signs.

    $$5\times 1=5$$

13. Add the calculated products to obtain this entry.

    $$2+5=7$$

14. Entry (2,1): pair row 2 with column 1 and add their products.

    $$2\times 1+4\times 3$$

15. Calculate this individual product, including its signs.

    $$2\times 1=2$$

16. Calculate this individual product, including its signs.

    $$4\times 3=12$$

17. Add the calculated products to obtain this entry.

    $$2+12=14$$

18. Entry (2,2): pair row 2 with column 2 and add their products.

    $$2\times 2+4\times 1$$

19. Calculate this individual product, including its signs.

    $$2\times 2=4$$

20. Calculate this individual product, including its signs.

    $$4\times 1=4$$

21. Add the calculated products to obtain this entry.

    $$4+4=8$$

22. Entry (2,3): pair row 2 with column 3 and add their products.

    $$2\times 2+4\times 1$$

23. Calculate this individual product, including its signs.

    $$2\times 2=4$$

24. Calculate this individual product, including its signs.

    $$4\times 1=4$$

25. Add the calculated products to obtain this entry.

    $$4+4=8$$

26. Entry (3,1): pair row 3 with column 1 and add their products.

    $$1\times 1+6\times 3$$

27. Calculate this individual product, including its signs.

    $$1\times 1=1$$

28. Calculate this individual product, including its signs.

    $$6\times 3=18$$

29. Add the calculated products to obtain this entry.

    $$1+18=19$$

30. Entry (3,2): pair row 3 with column 2 and add their products.

    $$1\times 2+6\times 1$$

31. Calculate this individual product, including its signs.

    $$1\times 2=2$$

32. Calculate this individual product, including its signs.

    $$6\times 1=6$$

33. Add the calculated products to obtain this entry.

    $$2+6=8$$

34. Entry (3,3): pair row 3 with column 3 and add their products.

    $$1\times 2+6\times 1$$

35. Calculate this individual product, including its signs.

    $$1\times 2=2$$

36. Calculate this individual product, including its signs.

    $$6\times 1=6$$

37. Add the calculated products to obtain this entry.

    $$2+6=8$$

38. Place the calculated entries in their original row and column positions.

    $$\left[\begin{array}{ccc}16& 7& 7\\ 14& 8& 8\\ 19& 8& 8\end{array}\right]$$

Answer

The final answer is shown below.