Mathematics 10 — Exercise 3.4 · Q1 (iv) BA

Full question

Find BA, if possible.

Step-by-step solution

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

   $$(\left[\begin{array}{ccc}-1& 4& 1\\ 2& 3& 1\end{array}\right],\left[\begin{array}{cc}1& 2\\ -1& 1\\ 3& 0\end{array}\right])$$

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

   $$-1+4\times \left(-1\right)+1\times 3$$

3. Calculate this individual product, including its signs.

   $$\left(-1\right)\times 1=-1$$

4. Calculate this individual product, including its signs.

   $$4\times \left(-1\right)=-4$$

5. Calculate this individual product, including its signs.

   $$1\times 3=3$$

6. Calculate this operation before combining the remaining terms.

   $$\left(-1\right)\times 4=-4$$

7. Add the calculated products to obtain this entry.

   $$-1-4+3=-2$$

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

   $$-2+4\times 1+1\times 0$$

9. Calculate this individual product, including its signs.

   $$\left(-1\right)\times 2=-2$$

10. Calculate this individual product, including its signs.

    $$4\times 1=4$$

11. Calculate this individual product, including its signs.

    $$1\times 0=0$$

12. Add the calculated products to obtain this entry.

    $$-2+4+0=2$$

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

    $$2\times 1+3\times \left(-1\right)+1\times 3$$

14. Calculate this individual product, including its signs.

    $$2\times 1=2$$

15. Calculate this individual product, including its signs.

    $$3\times \left(-1\right)=-3$$

16. Calculate this individual product, including its signs.

    $$1\times 3=3$$

17. Calculate this operation before combining the remaining terms.

    $$\left(-1\right)\times 3=-3$$

18. Add the calculated products to obtain this entry.

    $$2-3+3=2$$

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

    $$2\times 2+3\times 1+1\times 0$$

20. Calculate this individual product, including its signs.

    $$2\times 2=4$$

21. Calculate this individual product, including its signs.

    $$3\times 1=3$$

22. Calculate this individual product, including its signs.

    $$1\times 0=0$$

23. Add the calculated products to obtain this entry.

    $$4+3+0=7$$

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

    $$\left[\begin{array}{cc}-2& 2\\ 2& 7\end{array}\right]$$

Answer

The final answer is shown below.