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 .