- #1
charlies1902
- 162
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I think I know the answer to these questions, but I just want to make sure.
1) If A is invertible then A+A is invertible. True/False
True.
Because det(A)≠0, det(A+A)=det(2A)=2^n * det(A)≠0
Is this correct.
2) A 3x3 matrix can have 2 distinct eigenvalues. True/False
True, although I was kind of confused with what "distinct" means.
The characteristic polynomial can look something like this: (λ-1)^2 * (λ+2)
Distinct just refers to the # of "different" eigenvalues right? And doesn't include them again if they're repeated?
1) If A is invertible then A+A is invertible. True/False
True.
Because det(A)≠0, det(A+A)=det(2A)=2^n * det(A)≠0
Is this correct.
2) A 3x3 matrix can have 2 distinct eigenvalues. True/False
True, although I was kind of confused with what "distinct" means.
The characteristic polynomial can look something like this: (λ-1)^2 * (λ+2)
Distinct just refers to the # of "different" eigenvalues right? And doesn't include them again if they're repeated?