Three planes have the following equations...

Not sure on how to approach this question..

- February 26th 2011, 04:59 PMOilerFind all values of K for which the system of linear equations..
Three planes have the following equations...

Not sure on how to approach this question.. - February 26th 2011, 05:12 PMAckbeet
I would work with determinants. Check this thread out. That might give you a few ideas. Make sure to read all the way to the end, if you're interested in a rigorous proof, as you can see that my first idea was invalid.

- February 27th 2011, 05:26 AMHallsofIvy
This can't be right. In reducing the first two columns, you will get a term involving k in the third column of the third row (I get "k- 6"), then have to divide by that term. You should have a "k" in the denominator.

Quote:

Not sure on how to approach this question..

- February 27th 2011, 09:11 AMLoblawsLawBlog
I solved this using Maxima and its answer agrees with Oiler's reduced echelon form.

Just use that form to get expressions for your variables, Oiler. You can read them right off. Looking at the last row, what's z? Then find x and y similarly (these depend on k). Is there any k that won't give an answer, or will give more than one answer? - February 27th 2011, 09:28 AMPlato
- February 27th 2011, 11:11 AMLoblawsLawBlog
Oops, I answered without thinking this through. It looks like those programs cancel factors in the denominators. If it's reduced manually then there are ways to get more than one solution.