Find a 3x1 matrix X with entries not all zero such that AX =3X ,

where

A= (1,2 ,-1)

(1,0 ,1)

(4,-4,5)

Question

NinasiaChyn3ao5rtely NinasiaChyn3ao5rtely

26-11-2016
Mathematics

Answered

Find a 3x1 matrix X with entries not all zero such that AX =3X ,

where

A= (1,2 ,-1)

(1,0 ,1)

(4,-4,5)

Verified Answer :

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syed514 syed514 · Answer 1 · 2016-12-02T09:25:58-05:00

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 =

Solve that in the normal way to find the vector X.

Find a 3x1 matrix X with entries not all zero such that AX =3X , whereA= (1,2 ,-1)(1,0 ,1)(4,-4,5)

Verified Answer :

Related Questions

Find a 3x1 matrix X with entries not all zero such that AX =3X ,

where

A= (1,2 ,-1)

(1,0 ,1)

(4,-4,5)