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**1.**

1) Given 2x2 matrix A with A^t = A. How many linearly independent eigenvectors is A?

2) Is a square matrix with zero eigenvalue invertible?

**2;**When it comes to whether it is invertible; the det(A-λ* I) v = 0

where det (A-λ * I) v = 0 where λ = 0

We get Av = 0, where the eigenvector is zero. But this proves anything?

Or it is possible to prove that det(A) ≠ 0? Im not sure about how to prove it

I feel I lack some theory behind it all.

Im completely blank on the first, so thanks for all your help

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