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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?
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?

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chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0I created an augmented matrix, and got it to reduced row echelon form. Now how do I express that in vector notation?

chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0\[\left[\begin{matrix}1 & 0 & 0 &5 \\ 0 & 1 & 0 &7\\ 0 & 0 & 1 &9\end{matrix}\right]\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The solution vector is the last column of that matrix. The augmented matrix you've written is shorthand for \[\left[\begin{matrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{matrix}\right] \cdot \left[\begin{matrix}x \\y \\ z\end{matrix}\right] =\left[\begin{matrix}5 \\7\\ 9\end{matrix}\right] \]

chrisplusian
 one year ago
Best ResponseYou've already chosen the best response.0Thats 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.....\[(x,y,z)^T =\left(\begin{matrix}5 \\ 7\\ 9\end{matrix}\right)\] ?????
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