## chrisplusian one year ago When a problem says to solve a system using gaussian elimination and express the solution in "vector form", how do you express the result in vector form?

1. chrisplusian

I created an augmented matrix, and got it to reduced row echelon form. Now how do I express that in vector notation?

2. chrisplusian

$\left[\begin{matrix}1 & 0 & 0 &-5 \\ 0 & 1 & 0 &7\\ 0 & 0 & 1 &-9\end{matrix}\right]$

3. anonymous

The solution vector is the last column of that matrix. The augmented matrix you've written is shorthand for $\left[\begin{matrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix}\right] \cdot \left[\begin{matrix}x \\y \\ z\end{matrix}\right] =\left[\begin{matrix}-5 \\7\\ 9\end{matrix}\right]$

4. chrisplusian

Thats what is confusing me. Every time I have expressed a solution as a vector it has parameters, because there is at least one free variable. In this case there are no free variables and the RREF produces a solution that is geometrically interpreted as the point at which three planes intersect. So is the vector representation.....$(x,y,z)^T =\left(\begin{matrix}-5 \\ 7\\ 9\end{matrix}\right)$ ?????

5. chrisplusian

@Jemurray3

6. anonymous

Yes.