Mathematics 10 — Exercise Review · Q4 (i)

Full question

For the following vectors, find 5b−a+c.

Step-by-step solution

1. Multiply every matrix entry by the scalar.

   $$(5,\left[\begin{array}{c}3\\ 1\end{array}\right])$$

2. Entry (1,1): multiply its value by the scalar.

   $$5\times 3=15$$

3. Entry (2,1): multiply its value by the scalar.

   $$5\times 1=5$$

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

   $$\left[\begin{array}{c}15\\ 5\end{array}\right]$$

5. The orders match. Combine only entries in the same row and column.

   $$(\left[\begin{array}{c}15\\ 5\end{array}\right],\left[\begin{array}{c}2\\ -1\end{array}\right])$$

6. Entry (1,1): subtract the corresponding entries.

   $$15-2=13$$

7. Entry (2,1): subtract the corresponding entries.

   $$5+1=6$$

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

   $$\left[\begin{array}{c}13\\ 6\end{array}\right]$$

9. The orders match. Combine only entries in the same row and column.

   $$(\left[\begin{array}{c}13\\ 6\end{array}\right],\left[\begin{array}{c}4\\ 1\end{array}\right])$$

10. Entry (1,1): add the corresponding entries.

    $$13+4=17$$

11. Entry (2,1): add the corresponding entries.

    $$6+1=7$$

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

    $$\left[\begin{array}{c}17\\ 7\end{array}\right]$$

13. The first component multiplies î, the second multiplies ĵ.

    $$17\times î+7\times ĵ$$

Answer

The final answer is shown below.