Need help with linear algebra

[Zetsan]

I'm learning linear algebra and I almost understand nothing... My teacher said we would have questions like this on the exam. Can anyone explain me how do we solve theses questions? It would save my life!

 

[Deleted member 4993]

I'm learning linear algebra and I almost understand nothing... My teacher said we would have questions like this on the exam. Can anyone explain me how do we solve theses questions? It would save my life!

View attachment 26073

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem.

 

[Steven G]

First step is to find what is called the characteristic equation.

Compute | A - L*I |=0. Just subtract lambda from each entry on the diagonal leaving all the other entries the same. Then compute this determinant and set it equal to 0. This will yield a polynomial in the variable lambda. This is the characteristic equation.

2nd step: Solve this equation for Lambda. This will be your eigenvalue.

Post back showing your work and we'll go from there.

 

[HallsofIvy]

\(\displaystyle \lambda\) is an "eigenvalue" of linear transformation, A, if and only if there exist a non-zero vector, v, such that \(\displaystyle Av= \lambda v\). From that \(\displaystyle Av- \lambda v= (A- \lambda I)v= 0\). And that means that the determinant of \(\displaystyle A- \lambda I\) must be 0.