(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the following linear system of equations:

x_{1}+2x_{3}-5x_{4}= 0

x_{1}+ 4x_{2}+4x_{3}– 5x_{4}= 10

x_{1}+ 2x_{2}+ 3x_{3}– 5x_{4}= 5

4x_{1}+ 2x_{2}+ 9x_{3}– 20x_{4}= 5

b) Solve the equation system with the Gaussian method.

c) The solution set describes a plane. Specify it in the parameter form.

2. Relevant equations

Parameter form: [itex]\vec{r}[/itex]= [itex]\vec{r}[/itex]_{0}+ λ[itex]\vec{v}[/itex] + β[itex]\vec{w}[/itex]

3. The attempt at a solution

3. My Work

After Gauss?:

1 2 0 -5 0

0 2 4 0 10

0 0 3 0 5

0 0 0 0 0

Rank is 3 so there is one free chooseable variable. I chose x4 and ended with the equation:

[itex]\vec{X}[/itex] =

[tex]\begin{vmatrix}-10/3\\5/3\\5/3\\0\end{vmatrix}[/tex] + [itex]\vec{x}[/itex]_{4}* [tex]\begin{vmatrix}5\\0\\0\\1\end{vmatrix}[/tex]

Which I think is the plane’s formula? I’m not totally sure. My teacher said that he wouldn’t be putting the answers up, so I wanted a second opinion on my numbers. Please and thank you.

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# Homework Help: Linear Algebra: Linear Equation System -> Parameter Form

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