A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

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?

  • This Question is Closed
  1. chrisplusian
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  2. chrisplusian
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

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

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    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
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @Jemurray3

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes.

  7. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.