Problem 2.5 a
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Perhaps you can help me with my confusion about this problem. It appears in the r2-2r1 step, your solution accidentally performed -A24-2A14 to get a value of -3 for A24 instead of A24-2A14 to get a 7 for A24. I don't think the correct solution is not an empty solution set. There are four equations and four unknowns and the solution is [x1 x2 x3 x4]T = [26/15 -13/30 2/5 -1/10]T. Am I thinking about this the wrong way?
I think so. A24 is 7 after subtraction
No, his answer is correct. (-)2/1 = -2, so you multiply row 1 by -2 and add that to row 2. Same thing for row 3, and for row four, you'll multiply row 1 by (-5)/1 = -5, and add that to row 4. It's step 7 listed here: https://www.statlect.com/matrix-algebra/Gaussian-elimination