Question

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

Answer 1

`9u-6v=\langle-87, 33\rangle`

Explanation:

In order to sum the vector
`u` and the vector
`v` , it is convenient to define some operations.

The vector addition is given by:

`u \pm v = \langle u_1 \pm v_1 , u_2\pm v_2 ,..,u_n\pm v_n\rangle`

And the scalar multiplication is given by:

`ku=k \langle u_1 ,u_2,..., u_n\rangle =\langle k u_1, k u_2,..., k u_n \rangle`

Using the previous definitions, let's solve the problem.

First, let's find
`9u` :

`9u=9 \langle -5,1 \rangle =\langle 9*(-5), 9*(1)\rangle=\langle-45, 9\rangle`

Now, let's find
`6v` :

`6v=6\langle 7,-4 \rangle =\langle 6*(7), 6*(-4)\rangle=\langle42, -24\rangle`

Finally, let's find
`9u-6v`:

`9u-6v=\langle-45, 9\rangle - \langle42, -24\rangle =\langle-45 -42, 9-(-24)\rangle=\langle-87, 33\rangle`

Answer 2

9u -6v = 9&lt;-5, 1> -6&lt;7, -4>
.. = &lt;9*-5 -6*7, 9*1 -6*-4>
.. = &lt;-87, 33>