Mathematics 10 — Exercise 3.4 · Q1 (iii) AB

Full question

Find AB, 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.

   $$(\left[\begin{array}{c}4\\ 4\end{array}\right],\left[\begin{array}{cc}2& 5\end{array}\right])$$

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

   $$4\times 2$$

3. Calculate this individual product, including its signs.

   $$4\times 2=8$$

4. Add the calculated products to obtain this entry.

   $$8=8$$

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

   $$4\times 5$$

6. Calculate this individual product, including its signs.

   $$4\times 5=20$$

7. Add the calculated products to obtain this entry.

   $$20=20$$

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

   $$4\times 2$$

9. Calculate this individual product, including its signs.

   $$4\times 2=8$$

10. Add the calculated products to obtain this entry.

    $$8=8$$

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

    $$4\times 5$$

12. Calculate this individual product, including its signs.

    $$4\times 5=20$$

13. Add the calculated products to obtain this entry.

    $$20=20$$

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

    $$\left[\begin{array}{cc}8& 20\\ 8& 20\end{array}\right]$$

Answer

The final answer is shown below.