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Calculus and Beyond Homework Help
Finding a Unique Solution to a System of Equations
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[QUOTE="The Head, post: 6409984, member: 321011"] [B]Homework Statement:[/B] Find when the system of equations is unique: x-y-2z-2w= 3 y+z+w= 4a+3 z+3w= -4a-4 (-a+2)w= b+4a^2-4a-7 [B]Relevant Equations:[/B] Full Rank = Unique It makes sense that a=2 would cause problems because then we wouldn't have a matrix of full rank and we'd be unable to determine a value for w. But the key also says that when b+4a^2-4a-7≠0. Why is that an issue? For example, if a=1, that just says implies that w=0. Through back-subsitution, we get z=-8, y=15, x=2. And the solution: (2, 15,-8, 0) is unique still because it's the only possible solution, right? What am I missing here? [/QUOTE]
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Finding a Unique Solution to a System of Equations
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