Question

Given vectors a=(-2, 1) and b = (5, 4), find 5a - 3b.Write your answer in component form.5a - 3b = (0)X 5? ?

Answer 1

In order to find 5a-3b, lets find 5a. This is given by

`\begin{gathered} 5a=5(-2,1) \\ 5a=(-10,5) \end{gathered}`

Similarly, -3b is given by

`\begin{gathered} -3b=-3(5,4) \\ -3b=(-15,-12) \end{gathered}`

Then, by substituting our results into the expression 5a-3b, we get

`5a-3b=(-10,5)+(-15,-12)`

This can can be done by adding entry by entry, that is

`5a-3b=(-10-15,\text{ 5-12)}`

Therefore, the answer is

`5a-3b=(-25,-7)`