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!