Question

Let u = <-5, 1>, v = <7, -4>. Find 9u - 6v.

Answer 1

9u <-- scalar multiplication, same for 6v
9u - 6v <---- vector addition

do the scalar mutiplication first, to get a resultant vector
then "add" them up, or subtract in this case

Answer 2

You might get annoyed, but I'm new to this topic, so I don't know what to do. Maybe baby steps? :)

Answer 3

one sec

Answer 4

Sure thing.

Answer 5

\(\bf {
\begin{array}{llll}
u=<-5,1>\\
v=<7,-4>
\end{array}\qquad
\begin{array}{llll}
9u\implies <9\cdot -5,9\cdot 1>\implies <-45,9>\\
-6v\implies <-6\cdot 7,-6\cdot 4>\implies <-42,24>
\end{array}
\\ \quad \\
9u-6v\implies <-45,9> + <-42,24>\\ \quad \\ <-45+(-42)\quad ,\quad 9+24>
}\)

Answer 6

well... could have been done using the - I gather

Answer 7

Ohhh, so does it look like I'm distributing 9u to the first one (u), and -6v to v?

Answer 8

And the answer is <-87, 33>?

Answer 9

yeap

Answer 10

Thank you so much! It became clear now. :)

Answer 11

\(\begin{array}{llll}
u=<-5,1>\\
v=<7,-4>
\end{array}\qquad
\begin{array}{llll}
9u\implies <9\cdot -5,9\cdot 1>\implies <-45,9>\\
6v\implies <6\cdot 7,6\cdot 4>\implies <42,-24>
\end{array}
\\ \quad \\
9u-6v\implies <-45,9> - <42,-24>\implies <-45-42\quad ,\quad 9-(-24)>\)

would have done the same thing anyhow

Answer 12

yw