Use D l1 0 p 0 0 l2 p 0 ( ( 0 0 p ln and (3) to show that eDt el1t 0 p 0 0 el2t p 0 ( (
Chapter 10, Problem 24(choose chapter or problem)
Use \(\mathbf{D}=\left(\begin{array}{cccc}\lambda_{1} & 0 & \cdots & 0 \\ 0 & \lambda_{2} & \cdots & 0 \\ \vdots & & & \vdots \\ 0 & 0 & \cdots & \lambda_{n}\end{array}\right)\) and (3) to show that \(e^{\mathbf{D} t}=\left(\begin{array}{cccc} e^{\lambda_{1} t} & 0 & \cdots & 0 \\ 0 & e^{\lambda_{2} t} & \cdots & 0 \\ \vdots & & & \vdots \\ 0 & 0 & \cdots & e^{\lambda_{n} t} \end{array}\right) \).
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