Question

Find a 3x1 matrix X with entries not all zero suchthatAX =3X , where
A= (1,2 ,-1)
(1,0 ,1)
(4,-4,5)

Answer 1

\[ㅇㄹㄴㅁㄴㅇㄹ\nu \theta \Gamma \Psi \mathbb{Z}^-\delta\]

Answer 2

This is called an eigenvector problem. If you search on wikipedia or something you'll find some solutions. I haven't done these for a while, but I think usually they don't give you the 3...

AX = 3X, then
AX - 3X = 0
(A-3I)X = 0
I is the identity matrix, which is 3*3 in dimensions. Now you can work out the matrix A-3I.
3I = [3, 0, 0
0,3,0
0,0,3 ]
So, calculate A-3I. Now you just have the type of problem which is BX = 0. Solve that in the normal way to find the vector X.

Answer 3

trivial solution would be 3x1 zero matrix

Answer 4

all solutions are multiples of [-1/4, 1/4, 1]. You can get that if you follow the method above.

Answer 5

given matrix, eigen value, and find eigen vector huh??

Answer 6

http://www.wolframalpha.com/input/?i=matrix+eigenvalues&a=*C.matrix+eigenvalues-_*Calculator.dflt-&f2=%7B%7B1%2C2+%2C-1%7D%2C+%7B1%2C0+%2C1%7D%2C+%7B4%2C-4%2C5%7D%7D&x=2&y=9&f=MatrixOperations.theMatrix_%7B%7B1%2C2+%2C-1%7D%2C+%7B1%2C0+%2C1%7D%2C+%7B4%2C-4%2C5%7D%7D

scarydoor is right