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Reduced a big matrix, now the parametric form is not right, :\

  • Thread starter mr_coffee
  • Start date
  • #1
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Hello everyone I did the following problem:
Click http://img220.imageshack.us/img220/8486/untitled1copy4oq.jpg [Broken] to view the problem and my answer.

The row reduced form is:
1 5 0 0 -7 6 -7
0 0 1 0 -1 1 -1
0 0 0 1 - 2 -4 8

Any help would be great
 
Last edited by a moderator:

Answers and Replies

  • #2
TD
Homework Helper
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Your matrix seems to be correct, and is:

[tex]\left( {\begin{array}{*{20}c}
1 & 5 & 0 & 0 & { - 7} & 6 &\vline & { - 7} \\
0 & 0 & 1 & 0 & { - 1} & 1 &\vline & { - 1} \\
0 & 0 & 0 & 1 & { - 2} & { - 4} &\vline & 8 \\

\end{array} } \right)[/tex]

Now we have 3 lineair indepedant equations with 6 variables which means we can 'choose' 3 variables. We keep the variables [tex]x_1[/tex], [tex]x_3[/tex] and [tex]x_4[/tex]. Let [tex]x_2 = s[/tex], [tex]x_5 = t[/tex] and [tex]x_6 = u[/tex].

This gives the solution of the system:

[tex]\left\{ \begin{gathered}
x_1 + 5s - 7t + 6u = - 7 \hfill \\
x_3 - t + u = - 1 \hfill \\
x_4 - 2t - 4u = 8 \hfill \\
\end{gathered} \right. \Leftrightarrow \left\{ \begin{gathered}
x_1 = - 7 - 5s + 7t - 6u \hfill \\
x_3 = - 1 + t - u \hfill \\
x_4 = 8 + 2t + 4u \hfill \\
\end{gathered} \right[/tex]

Can you put it in vectorial notation now?
 
  • #3
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1
hm...i don't see how 'im still missing this:
i entered in:
-7 -5 7 6
0 1 0 0
-1 0 1 -1
8 0 0 4
0 0 1 0
0 0 0 1

still wrong, thanks for the reply!
 
  • #4
TD
Homework Helper
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I think you for got the 2 in column 3 for [itex]x_4[/itex] since that has "2t) in its solution.
 
  • #5
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1
I'm stilling screwing somthing up...I fixed what you said, but still not the right answer, and I know its row reduced correctly because I checked it with my calculator! here is the picture of what I wrote and submitted:
http://img214.imageshack.us/img214/8780/gfsdgfd6wq.jpg [Broken] Thanks for the help!
 
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  • #6
TD
Homework Helper
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I see you entered "6" in the last column for [itex]x_1[/itex] and I think that has to be "-6" (check my last system).
 
  • #7
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1
ah ha! my bad! thanks for the help! :biggrin:
 
  • #8
TD
Homework Helper
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It was correct now? Glad I could help :smile:
 

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