(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let B =

|1 -2|

|1 3 |

Let C =

|1 4 0|

|0 1 0|

|0 0 2|

Finde[itex]^{B}[/itex] ande[itex]^{C}[/itex]

2. Relevant equations

e[itex]^{A}[/itex] = [itex]\Sigma[/itex]x[itex]^{n}[/itex]/n!

e[itex]^{A}[/itex] = P[itex]^{-1}[/itex]e[itex]^{D}[/itex]P

3. The attempt at a solution

My professor told me the first step to approaching these types of problems is to find the eigenvalues for both B and C. For B, I get eigenvalues 2+iand 2-i, and I get 1 (double root) and 2 as the eigenvalues for C.

I'm having trouble finding some eigenvectors for B (my teacher did not provide any sufficient or clear examples of eigenstuff involving complex numbers), and I get [1, 0, 0] and [0, 0, 1] as my eigenvectors for C (for e-values 1 and 2, respectively).

I'm sure at this point I'm supposed to construct P, P[itex]^{-1}[/itex] and D for each and somehow use those to finde[itex]^{B}[/itex] ande[itex]^{C}[/itex], but I'm not sure how to go about doing that since my professor did not clearly explain the entire process...

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# Homework Help: Matrix Exponentials

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