Ordinary differential equations involving matrices

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ricky786
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hi i got the eigen values as e=-1, e=i, -i as the imaginary roots and both 1 multiplicities can some one complete the question please

thanks
 
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  • Typeset problem: show that x-dot = Ax on R^3 with A the 3x3 matrix rows (-1,0,0), (0,0,1), (0,-1,0) has general solution x(t) = Ae^(-t), y(t) = B cos t + C sin t, z(t) = C cos t - B sin t, with A, B, C real constants.
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Welcome to PF!

Hi ricky786! Welcome to PF! :smile:
ricky786 said:
hi i got the eigen values as e=-1, e=i, -i as the imaginary roots and both 1 multiplicities can some one complete the question please

thanks

Hint: If the eigenvalues are -1 and ±i, then there's a basis in which x' = -x, y' = iy, z' = -iz …

now solve. :wink:​