Find a basis for the eigenspace corresponding to each listed eigenvalue.

dictetzqh 2021-11-21 Answered

Find a basis for the eigenspace corresponding to each listed eigenvalue.
A=[5021],λ=1,5

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Expert Answer

Florence Pittman
Answered 2021-11-22 Author has 15 answers

To get the basis for the eigenspace, we first solve the system (Aλl)x=0
For λ=1,Al=
[510211]
[4020]
The augment matrix of (Al)x=0 is
[400200]
With x1=0 and x2 is free, the solution can be written in the form:
x=x2
[01]
So [01]
Is a basis for the eigenspace.
For λ=5,A5l=
[550215]=[0024]
The augmented matrix of (A-5l)x=0 is
[000240]
That leads to 2x14x2=0x1=2x2. The solution can be writtem in the form:
x=x2
[21]
So
[21]
is a basis for the eigenspace.

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