3. For the system of linear differential equations below find the eigenvalues and eigen vectors of the coefficient matrix. Construct the fundamental set of solutions. 2 y' = [ 4 ] y

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Q: Prove by induction: "For all \( n \in \mathbb{N} \), \( \sum_{k=1}^{n} k \cdot k! = (n+1)! - 1 \).

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Q: Q3.3

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