find the eigenvalues and (right/column) eigenvectors of the matrix
A= |2 -1 |
|3 -2 |

AND

Express the vector | 3 |
| 5 | as a linear combination of the eigenvectors of A.


not asking for someone to give me the answer, just trying to understand the process.

1/24/2007 1:33:20 PM

The following statements are equivalent.

i) c is a characteristic value of A
ii)det(A-cI)=0.

were I is the identity matrix.

That should get you started.

1/24/2007 1:54:55 PM

yeah, solve the polynomial generated by det(A-lambda*I)=0, and that will give you the eigen values. plug those back in to get the eigen vectors.

1/24/2007 2:01:53 PM

ok for the first part i got the eigen values to be (1,-1)... that checked out when I did the calculations on matlab....

but when I plug them back in, trying to get the eigenvectors, I got (1,-1/3) for -1 and (1,-1) for +1. matlab says the answer is (1,3) and (1,1) respectively. Can anyone show me where I am going wrong... also... still need help on the 2nd part of my first question.

Thanks

1/24/2007 8:50:52 PM

you're almost there. The vectors that you found were just the top row of your row reduced matrix. What you need is a vector x such that when you multiply x by your row reduced matrix, you get zero.

1/24/2007 10:47:28 PM