Mathematics 10 — Exercise 3.4 · Q1 (ii) BA

Full question

Find BA, if possible.

Step-by-step solution

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

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

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

   $$3\times 1$$

3. Calculate this individual product, including its signs.

   $$3\times 1=3$$

4. Add the calculated products to obtain this entry.

   $$3=3$$

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

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

6. Calculate this individual product, including its signs.

   $$3\times \left(-2\right)=-6$$

7. Add the calculated products to obtain this entry.

   $$-6=-6$$

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

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

9. Calculate this individual product, including its signs.

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

10. Add the calculated products to obtain this entry.

    $$-4=-4$$

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

    $$\left(-4\right)\times \left(-2\right)$$

12. Calculate this individual product, including its signs.

    $$\left(-4\right)\times \left(-2\right)=8$$

13. Add the calculated products to obtain this entry.

    $$8=8$$

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

    $$\left[\begin{array}{cc}3& -6\\ -4& 8\end{array}\right]$$

Answer

The final answer is shown below.