Eagerissac
New member
- Joined
- Jan 9, 2020
- Messages
- 16
Can anyone tell me what's wrong with the answers I gave for the question in the picture below? I calculated the eigenvalues and got 9 and 12.
Subtracting these values from the matrix, I'm left with these two matrices:
For λ = 9
[10-9 1 1 | 0]
[1 10-9 1 | 0]
[1 1 10-9 | 0]
RREF gives me:
[1 1 1 | 0]
[0 0 0 | 0]
[0 0 0 | 0]
This gives two basis vectors because there are 2 free variables x2 and x3:
[-1]
[1]
[0]
and
[-1]
[0]
[1]
For λ = 12
[10-12 1 1 | 0]
[1 10-12 1 | 0]
[1 1 10-12 | 0]
RREF gives me:
[1 0 -1 | 0]
[0 1 -1 | 0]
[0 0 0 | 0]
The gives the basis vector:
[1]
[1]
[1]
Normalizing these vectors I get:
√((-1)^2 + (1)^2 + 0^2) = √2
[1/√2]
[1/√2]
[0]
√((-1)^2 + 0 ^2 + (1)^2) = √2
[-1/√2]
[0]
[1/√2]
and
√((1)^2 + (1)^2 + (1)^2) = √3
[1/√3]
[1/√3]
[1/√3]
This formed my answer for the U matrix. My D matrix are just the eigenvalues I got. The system keeps marking my answer as wrong and I'm not sure why it's incorrect. Am I doing something wrong?
Subtracting these values from the matrix, I'm left with these two matrices:
For λ = 9
[10-9 1 1 | 0]
[1 10-9 1 | 0]
[1 1 10-9 | 0]
RREF gives me:
[1 1 1 | 0]
[0 0 0 | 0]
[0 0 0 | 0]
This gives two basis vectors because there are 2 free variables x2 and x3:
[-1]
[1]
[0]
and
[-1]
[0]
[1]
For λ = 12
[10-12 1 1 | 0]
[1 10-12 1 | 0]
[1 1 10-12 | 0]
RREF gives me:
[1 0 -1 | 0]
[0 1 -1 | 0]
[0 0 0 | 0]
The gives the basis vector:
[1]
[1]
[1]
Normalizing these vectors I get:
√((-1)^2 + (1)^2 + 0^2) = √2
[1/√2]
[1/√2]
[0]
√((-1)^2 + 0 ^2 + (1)^2) = √2
[-1/√2]
[0]
[1/√2]
and
√((1)^2 + (1)^2 + (1)^2) = √3
[1/√3]
[1/√3]
[1/√3]
This formed my answer for the U matrix. My D matrix are just the eigenvalues I got. The system keeps marking my answer as wrong and I'm not sure why it's incorrect. Am I doing something wrong?
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