Finding a Set of Basic Solutions to a Homogeneous System
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you can see that the second row is two third of the first row. so you really have one equation $$x  2y + 2z  3w = 0$$ you can let three variables, say, $y,z, w$ free. so you get the three basic solutions $$(2,1,0,0), (2,0,1,0), (3,0,0,1) $$ by setting one of the free variables to one and rest of them to zero.
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PTiger17
Updated on August 09, 2022Comments

PTiger17 over 1 year
$$\lceil3,6,6,9 \rceil$$ $$\lfloor 2, 4, 4, 6 \rfloor$$
For finding a set of basic solutions of the homogeneous system, I know it'll be $AX=0$ and begin by row reducing. The issue I run into is that the bottom row goes to all zeros and I'm unsure of how the text comes up with the three listed basic solutions.