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Mathematics
Linear and Abstract Algebra
1.3.11 Determine if b is a linear combination
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[QUOTE="Opalg, post: 6775983, member: 703375"] You want to know whether $b$ is a linear combination of $a_1$, $a_2$ and $a_3$. So you want to know whether the equation $xa_1 + ya_2 + za_3 = b$ can be solved for $x$, $y$ and $z$. The rref matrix tells you that this is equivalent to solving the equations $$x + 5z = 2,$$ $$y+4z=3$$ (two equations for three unknowns, so there should be plenty of solutions). Try taking it from there. [/QUOTE]
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Forums
Mathematics
Linear and Abstract Algebra
1.3.11 Determine if b is a linear combination
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