Question

Quick question
Let u = <3, -1>, v = <-6, -6>. Find 9u + 2v.

Answer 1

Would you add 3 +-6 then multiply by 9. Then add -1+-6 then multiply by 2 ? Or would add 3+-1 then multiply by 9 and then add -6 +-6 then multi by 2?

Answer 2

help plz :(

Answer 3

the notation \(\langle a,b\rangle\) is short for \(a\mathbb i+b\mathbb j\) where i and j are vectors. The property is,

Adding-
\(\langle a,b\rangle + \langle c,d\rangle = (a\mathbb i +b\mathbb j)+(c\mathbb i+d\mathbb j)=(a+c)\mathbb i+(b+d)\mathbb j =\langle a+c,b+d \rangle\) (which means only coefficients of the same vector can be summed together)

multiplying -
\(t\langle a,b\rangle=t(a\mathbb i+b\mathbb j)=(ta\;\mathbb i+tb\;\mathbb j)=\langle ta,tb \rangle\)

So when you are given \(t\langle a,b\rangle + u\langle c,d \rangle\) . Just as you do in normal algebra first multiply and then add

Answer 4

Thank you so much :)

Answer 5

you are welcome :)