Question

Let v be an eigenvector of a matrix A with a corresponding eigenvalue ?=2. Find one solution x of the system Ax=v.

Answer 1

Answer with explanation:

For, a Matrix A , having eigenvector 'v' has eigenvalue =2

 The order of matrix is not given.

It has one eigenvalue it means it is of order , 1×1.

→A=[a]

Determinant [a-k I]=0, where k is eigenvalue of the given matrix.

It is given that,

k=2

For, k=2, the matrix [a-2 I] will become singular,that is

→ Determinant |a-2 I|=0

→I=[1]

→a=2

Let , v be the corresponding eigenvector of the given eigenvalue.

→[a-I] v=0

→[2-1] v=[0]

→[v]=[0]

→v=0

Now, corresponding eigenvector(v), when eigenvalue is 2 =0

 We have to find solution of the system

→Ax=v

→[2] x=0

→[2 x] =[0]

→x=0, is one solution of the system.