Determinants

[czech09]

Well it's been a year since I've taken Calc/any type of math course (and there aren't any in my forseeable future). My cousin asked for help on a problem, I'd refer him to my friend however it's 2:20 here so I need anandtech to come to the rescue...

http://home.zcu.cz/~teskova/WWW-KMA/DCVME5.pdf

Problem 5.8.

Thanks to whoever can get this.

 

[orakle]

What is the question asking? Not everyone can read that language.

 

[czech09]

Originally posted by: orakle
What is the question asking? Not everyone can read that language.

Sorry about that - it's asking for what value of X that determinant is true (or if I should rephrase it concretely - for what value of X is the determinant = 0).

 

[esun]

Solve 5.8. It's pretty obvious without having to read anything. Now the determinant of a matrix is zero is the same as it having two of the same rows (since you can subtract rows in a matrix without altering the determinant except by some multiplicative factor, you can subtract the same rows to get a zero row reducing the determinant to zero).

So, if x = 1 or x = -1, the first two rows are the same. If x = 2 or x = -2 the bottom two rows are the same. There you go, that's the answer. If you go ahead and work out the whole determinant via minors and cofactors you should arrive at the same solution.

 

[czech09]

Originally posted by: esun
Solve 5.8. It's pretty obvious without having to read anything. Now the determinant of a matrix is zero is the same as it having two of the same rows (since you can subtract rows in a matrix without altering the determinant except by some multiplicative factor, you can subtract the same rows to get a zero row reducing the determinant to zero).

So, if x = 1 or x = -1, the first two rows are the same. If x = 2 or x = -2 the bottom two rows are the same. There you go, that's the answer. If you go ahead and work out the whole determinant via minors and cofactors you should arrive at the same solution.

Thanks I appreciate it! Cousin owes me now .

 

[orakle]

I figured thats what you had to do but thanks for making me sound like an idiot. I was never that good with the little tricks in linear algebra so I was going to do the cofactor expansion and solve but since you've already done it with a short cut, less work for me