Linear Algebra Question

[buckaroobill]

Okay so I have a matrix A corresponding to the L, the linear transformation which equals (-10a - c + 2d, 5a + b - d, 2c + d, 9a + 17b + 2d).

-10.21547311639418 is one of the eigenvalues of A. What effect does the transformation L have on the eigenvectors associated to -10.21547311639418 (Note that you don't need to do calculations to answer this question).

 

[mathcracker]

Okay so I have a matrix A corresponding to the L, the linear transformation which equals (-10a - c + 2d, 5a + b - d, 2c + d, 9a + 17b + 2d).

-10.21547311639418 is one of the eigenvalues of A. What effect does the transformation L have on the eigenvectors associated to -10.21547311639418 (Note that you don't need to do calculations to answer this question).

Let $\displaystyle A$ be the matrix determined by the linear transform $\displaystyle L$. Then, assume that $\displaystyle v$ is an eigenvector associated to $\displaystyle \lambda = -10.21547311639418$, then

$\displaystyle Lv = Av = \lambda v = -10.21547311639418 v$

So the effect is just simply multiplying by -10.21547311639418 .