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Problem:
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Let u=[-3,4] and v=[1,-1]. Find scalars s and t so that
the equation,
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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}
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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! |