Mathematics 10 — Exercise 6.2 · Q1 (iv)

Full question

For the following vectors, find b−a.

Step-by-step solution

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

   $$(\left[\begin{array}{c}1\\ 5\end{array}\right],\left[\begin{array}{c}7\\ -3\end{array}\right])$$

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

   $$1-7=-6$$

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

   $$5+3=8$$

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

   $$\left[\begin{array}{c}-6\\ 8\end{array}\right]$$

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

   $$-6\times î+8\times ĵ$$

Answer

The final answer is shown below.