1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Linear Algebra Question

  1. Nov 18, 2006 #1
    I have three systems of equations:
    x+y+2z=a , x+z= b and 2x+y+3z=c
    Show that in order for this system to have at least one solution, a,b,c must satisfy c=a+b.

    Obviously I can add the equations a and b and get c. But I dont know how else to approach showing this. I think the points of x,y,z of c must satisfy both a,b and provide a solution set for both but Im not sure how to prove that. HELP PLEASE~!
  2. jcsd
  3. Nov 19, 2006 #2
    The matrix system is:

    [tex] \begin{bmatrix}
    1 & 1 & 2 & a \\
    1 & 0 & 1 & b \\
    2 & 1 & 3 & c \\

    The system has at least one solution if the rank of the coefficient matrix equals the rank of the augmented matrix. Get the matrix to row-echleon form.
    Last edited: Nov 19, 2006
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Linear Algebra Question Date
Subspace question May 9, 2016
Linear Algebra -- Projection matrix question Apr 25, 2016
Linear Algebra Question Sep 11, 2015
Linear Transformations, Linear Algebra Question May 10, 2015
Simple matrix/linear algebra question, help Apr 28, 2015