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

Mathematics

Adrienne Wiley

30 May, 19:43

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)

+3

Answers (1)

Know the Answer?

Tyson Hunter · Answer 1

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.

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

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)