Math Question

RedArmy

Platinum Member
Mar 1, 2005
2,648
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So here I am doing my easy Diff Eq homework involving 2x2 matrices and finding the Eigen values and associated vectors when all of a sudden I come across a 3x3. While it doesn't seem like that big of a deal, it was quite a jump from what I was doing.

I know how to work the equation and everything, but I'm getting a different answers then what someone else is...and no one else I know has done it yet.

Therefore, is there an easier way to find an answer to this problem or do I have to try the problem a 3rd time.

For curious minds:

|30 -16 -22|
|36 -20 -26|
|12 -06 -09|

My equation (using x instead of lambda) came out to be: (x^3)-(x^2)-534x-10560. The other person who did this problem got 0 instead of 10560. I could just stick with my answer but I don't want to do synthetic division on that to find the roots (if there even are any) :(
 

Goosemaster

Lifer
Apr 10, 2001
48,777
3
81
rref():D

Add -1 times row 1 to row 2.
Add -2/5 times row 1 to row 3.
Add 1/10 times row 2 to row 3.
Scale row 3 by -5/3.
Add 4 times row 3 to row 2.
Add 22 times row 3 to row 1.
Scale row 2 by -1/4.
Add 16 times row 2 to row 1.
Scale row 1 by 1/3


:D
 

RedArmy

Platinum Member
Mar 1, 2005
2,648
0
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Originally posted by: Goosemaster
rref():D

Add -1 times row 1 to row 2.
Add -2/5 times row 1 to row 3.
Add 1/10 times row 2 to row 3.
Scale row 3 by -5/3.
Add 4 times row 3 to row 2.
Add 22 times row 3 to row 1.
Scale row 2 by -1/4.
Add 16 times row 2 to row 1.
Scale row 1 by 1/3


:D

:Q That's...different.
 

chuckywang

Lifer
Jan 12, 2004
20,139
1
0
All the rows are independent, so 0 is definitely not an eigenvalue.

EDIT: n/m, it is. the rows aren't independent.
 

Fenixgoon

Lifer
Jun 30, 2003
31,491
9,817
136
the sum of your eigenvalues is equal to the trace. the product of your eigenvalues is equal to the determinant. very helpful little facts :)
 

RedArmy

Platinum Member
Mar 1, 2005
2,648
0
0
Originally posted by: FleshLight
You don't happen to be at UCI do you?

No, it's probably just a coincidence that the same material is being taught.