1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Linear algebra (impact of solution of theory of linear equations)

  1. Jan 24, 2009 #1
    I am currently taking the first college level linear algebra course and have a question.

    Consider the system of equations:

    1 3 2 |1
    0 -4 5 |-23
    2 2 9 |t

    Find values of t for which solutions to this augmented matrix can be obtained. Explain the implications of this example in the theory of linear equations.

    Answer:

    I found that t=-21 and that the solution is of the form {x, y, z} = {-1/4(23z+65), 1/4(5z+23), z}. That much is correct. What I don't know is what the bold statement above is asking of me. Any help is appreciated. Thanks.
     
  2. jcsd
  3. Jan 24, 2009 #2

    Mark44

    Staff: Mentor

    In row-reducing this augmented matrix, I found that if t = -21, the system has no solution. For a different value of t, I found the solution you show.

    For implications of this example in the theory of linear equations, I'm not sure which implications the text author has in mind, but I would start with the geometric significance of your solution set.
     
  4. Jan 25, 2009 #3
    Thanks for the reply Mark44. Here is the work I did to find t.

    1 3 2 |1
    0 -4 5 |-23
    2 2 9 |t

    row reducing

    1 3 2 |1
    0 -4 5 |-23
    0 -4 5 |t-2

    1 3 2 |1
    0 -4 5 |-23
    0 0 0 |t-2+23

    1 3 2 |1
    0 -4 5 |-23
    0 0 0 |t+21

    It follows that t=-21 is necessary for the system to have a solution so that 0=0 in the last row. Did I miss something?

    I know that the system has an infinite number of solutions that depend on the value of z, but I am still not sure how this impacts the theory of linear equations. Probably because I am somewhat unfamiliar with the theory itself. The book isn't much help.

    I am guessing that the theory of linear equations states that the roots of each equation in the system are the same if the system has a solution, but in this case the existence and identity of the solution are restricted by t and z, respectively. Would that be on the right track? Thanks for the help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Linear algebra (impact of solution of theory of linear equations)
Loading...