# A simple Vector Equation

### Problem:

 Let u=[-3,4] and v=[1,-1]. Find scalars s and t so that the equation, s [0,-3] + t u = v is satisfied.

#### Solution:

 Enter the vectors,

> u := [-3,4]: v := [1,-1]:
 and write down the equation as,

> Eq := evalm(s*[0,3]+t*u) = v;

`                       Eq := [-3 t, 3 s + 4 t] = [1, -1]`
 in order for these two vectors to be equal they must have their coordinates the same. We therefore obtain a system of two equations with two unknows.

> Eq1 := lhs(Eq)[1] = rhs(Eq)[1];

`                                Eq1 := -3 t = 1`
> Eq2 := lhs(Eq)[2] = rhs(Eq)[2];
`                             Eq2 := 3 s + 4 t = -1`
 and the solution is:

> solut := solve({Eq1,Eq2},{s,t});

`                         solut := {s = 1/9, t = -1/3}`

##### Notice:
 In this simple case we could have just obtained the answer by simple inspection but the fancy way of grabbing the coordinates of the "left-hand-side-of-Eq" with lhs(Eq)[1] can still be used in more complicated problems with the same amount of writing!

Link to the commands in this file
Carlos Rodriguez <carlos@math.albany.edu>