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# Solving linear equations using matricies watch

1. Can someone please run me through how to solve these equations using eigenvalues and eigenvectors, using the two cases where alpha = -3 and +1.

Also I initially tried solving this using Gaussian elimination and Cramer's rule/theroy but it gave x,y,z=0 which I dont think is correct

Thanks
2. (Original post by DonnieBrasco)

Can someone please run me through how to solve these equations using eigenvalues and eigenvectors, using the two cases where alpha = -3 and +1.

Also I initially tried solving this using Gaussian elimination and Cramer's rule/theroy but it gave x,y,z=0 which I dont think is correct

Thanks
All sets of homogeneous linear equations have the trivial solution x,y,z=0.

But you have found values of alpha such that there is a non-trivial solution
3. As I understand it (pls correct me if I'm wrong)...

The non-trivial solution of a system of linear homogeneous equations is that vector which is transformed to the zero vector by the coefficient matrix.

The eigenvectors of a matrix are those vectors whose direction remains unchanged by that matrix (only their magnitude is changed).

So does that mean that one of the eigenvectors must be the non-trivial solution? (since transforming a vector to zero is only changing its magnitude)?

EDIT: although I guess that can only be true if one of the eigenvalues is zero
4. (Original post by ghostwalker)
x
Surely one of you clever mathematicians out there can do this?!
5. For linear equations in general

in the homogeneous case, the solution set is the eigenvector corresponding to the eigenvalue of zero

So it's still necessary to find the solution set using Gauss-Jordan elimination. I don't think there's any other way

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