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Calculus and Beyond Homework Help
Matrix/Inconsistency Problem.
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[QUOTE="noelo2014, post: 4752636, member: 497769"] [h2]Homework Statement [/h2] Determine the value(s) of k for which the system [FONT="Courier"] -2 1 -1 x 1 4 2 k . y = -4 k -1 1 z 2 [/FONT] (please excuse my formatting) [h2]Homework Equations[/h2] [h2]The Attempt at a Solution[/h2] On my first attempt I tried making an augmented matrix and row-reducing it, but it started to get really hairy and taking too long, (this is an exam question), so I figured there must be an easier way of solving it. One thing I noticed is that if I set k=2 then the first and third rows of the matrix are multiples of each other (r1=-r3), however the corresponding values in the result vector aren't, this would lead me to suspect that k=2 gives me an inconsistent system. IF I set k=-2 I notice the 2nd and 3rd rows are scalar multiples of each other (including the result). So I guess this is a case of linear dependence somewhere. In other words if I row-reduced the augmented matrix I'd have a row of zeros and case of one of the x/y/z being a multiple of another. Then I guess that leaves all other values of k to mean 1 solution Am I approaching this correctly? Have I just solved this? I have a test on Thursday and I'd appreciate any help or tips for looking at matrices and finding clues and short-cuts to solving them. If there's any experts on Linear Algebra reading, how would you approach this question? I'd love to know Regards Noel [/QUOTE]
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Matrix/Inconsistency Problem.
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