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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
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