Matrix algebra question.

[Orsorum]

Determine for which lambda (L) the following system of linear equations has a nonzero solution. For such a lambda, solve this system.

Lx1 - 3Lx2 + 2x3 = 0
x1 + x2 + x3 = 0
-x1 + x2 - Lx3 = 0

So... I took matrix algebra, but I don't remember anything specifically like this... is it like solving an eigenvalue problem?

 

[TuxDave]

What if you solve for L such that the determinant is nonzero? That's what comes to my mind first, haven't touched Linear Algebra in 3 years.

 

[Orsorum]

Values for L are -1.2808, 0.7808.

 

[Orsorum]

Originally posted by: Zakath15
Values for L are -1.2808, 0.7808.

So, for those two values, the matrix is singular... (duh, i suppose)... so do I just choose an arbitrary value for the determinant, solve for lambda, then replug that in to the original matrix and solve?

 

[TuxDave]

I guess so... heh. Pick any L other than those two values and solve? Sounds like a strange problem to me... but I guess that's what he wants?

 

[dighn]

Originally posted by: Zakath15
Determine for which lambda (L) the following system of linear equations has a nonzero solution. For such a lambda, solve this system.

Lx1 - 3Lx2 + 2x3 = 0
x1 + x2 + x3 = 0
-x1 + x2 - Lx3 = 0

So... I took matrix algebra, but I don't remember anything specifically like this... is it like solving an eigenvalue problem?

wht u have there is a homogenous system which has a trivial solution 000. in order to have a non-zero solution (infinite # of solutions actually) i think the determinant needs to be zero because if you row reduce everything, to have non-trvial solutions you need to have at least one row empty making the determinant 0

 

[Orsorum]

So for either of those two values of lambda, the conditions are satisfied?

 

[FatAlbo]

Bump for you.

 

[thawolfman]

la la la la la la bamba.....oh..wait....

 

[dighn]

Originally posted by: Zakath15
So for either of those two values of lambda, the conditions are satisfied?

yeah

 

[TuxDave]

Originally posted by: dighn

Originally posted by: Zakath15
Determine for which lambda (L) the following system of linear equations has a nonzero solution. For such a lambda, solve this system.

Lx1 - 3Lx2 + 2x3 = 0
x1 + x2 + x3 = 0
-x1 + x2 - Lx3 = 0

So... I took matrix algebra, but I don't remember anything specifically like this... is it like solving an eigenvalue problem?

wht u have there is a homogenous system which has a trivial solution 000. in order to have a non-zero solution (infinite # of solutions actually) i think the determinant needs to be zero because if you row reduce everything, to have non-trvial solutions you need to have at least one row empty making the determinant 0

I see what you mean. For a zero determinant, you will generate an infinite number of solutions. But for a non-zero determinant, you may have a situation of having nonzero solutions or only a trivial solution. Perhaps looking at the determinant is not the right approach.

Ahh... my bad... didn't see that they all equal 0.

Edit: Can't Spell

 

[dighn]

Originally posted by: TuxDave

Originally posted by: dighn

Originally posted by: Zakath15
Determine for which lambda (L) the following system of linear equations has a nonzero solution. For such a lambda, solve this system.

Lx1 - 3Lx2 + 2x3 = 0
x1 + x2 + x3 = 0
-x1 + x2 - Lx3 = 0

So... I took matrix algebra, but I don't remember anything specifically like this... is it like solving an eigenvalue problem?

wht u have there is a homogenous system which has a trivial solution 000. in order to have a non-zero solution (infinite # of solutions actually) i think the determinant needs to be zero because if you row reduce everything, to have non-trvial solutions you need to have at least one row empty making the determinant 0

But for a non-zero determinant, you may have a situation of having nonzero solutions or only a trivial solution. Perhaps looking at the determinant is not the right approach.

Edit: Can't Spell

yeah. but the system is homogenous. therefore the trivial solution is always a solution. so the only way to have nontrivial solution(s) is if you have infinite number of solutions. or in other words a determinant of 0

 

[TuxDave]

Originally posted by: dighn

Originally posted by: TuxDave

Originally posted by: dighn

Originally posted by: Zakath15
Determine for which lambda (L) the following system of linear equations has a nonzero solution. For such a lambda, solve this system.

Lx1 - 3Lx2 + 2x3 = 0
x1 + x2 + x3 = 0
-x1 + x2 - Lx3 = 0

So... I took matrix algebra, but I don't remember anything specifically like this... is it like solving an eigenvalue problem?

wht u have there is a homogenous system which has a trivial solution 000. in order to have a non-zero solution (infinite # of solutions actually) i think the determinant needs to be zero because if you row reduce everything, to have non-trvial solutions you need to have at least one row empty making the determinant 0

But for a non-zero determinant, you may have a situation of having nonzero solutions or only a trivial solution. Perhaps looking at the determinant is not the right approach.

Edit: Can't Spell

yeah. but the system is homogenous. therefore the trivial solution is always a solution. so the only way to have nontrivial solution(s) is if you have infinite number of solutions. or in other words a determinant of 0

Gotcha... good thinking