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I'm attempting to teach myself linear algebra using this book http://joshua.smcvt.edu/linearalgebra/book.pdf

One of the exercises is:

What conditions must the constants, the b’s, satisfy so that each of these systems has a solution? Hint. Apply Gauss’s Method and see what happens to the right side.  x - 3y = b1 3x + y = b2 x + 7y = b3 2x + 4y = b4 

The answer given is

Gauss’s Method shows that this system is consistent if and only if both b3 = -2b1 + b2 and b4 = -b1 + b2. 

I've applied Gauss elimination and gotten

1x - 3y = b1 10y = -3b1 + b2 0y  = 2b1 - b2 + b3 0y  = b1 - b2 + b4 

But I still don't understand how the answer is deduced..

Someone help?

Thanks!

  • 1
    The 3rd and 4th equations you got via Gaussian elimination --- look at them closely --- aren't they the same as what's in the answer you were given?2012-11-08
  • 0
    Note that $0.y=0$, if you have missed it somehow. Then take the $b_4$ at left hand side....do similar for the 3rd equation.2012-11-08

1 Answers 1