Spanning set.

• Dec 5th 2009, 05:22 PM
Spanning set.
a) Show that the set of vectors {u1 = <1 2 -1>, u2 = <-1 -1 0>, u3= <2 5 4>} spans R^3

b)Express the vector v = <1 3 -2> in terms of the spanning set in part a).

By expressing does that mean I should just include the vector v in the set of given vectors? I'm not really sure with this one. Please help me. thanks!
• Dec 5th 2009, 05:26 PM
Chris L T521
Quote:

a) Show that the set of vectors {u1 = <1 2 -1>, u2 = <-1 -1 0>, u3= <2 5 4>} spans R^3

b)Express the vector v = <1 3 -2> in terms of the spanning set in part a).

By expressing does that mean I should just include the vector v in the set of given vectors? I'm not really sure with this one. Please help me. thanks!

Reduce the augmented matrix $\begin{bmatrix}1 &-1 & 2 & 1\\ 2 & -1 & 5 & 3\\ -1 & 0 & 4 & -2\end{bmatrix}$ and you'll find the constants a,b,c such that $a\left<1,2,-1\right>+b\left<-1,-1,0\right>+c\left<2,5,4\right>=\left<1,3,-2\right>$
• Dec 5th 2009, 05:50 PM