Maths WorkshopMaths problems with full solutions

Linear systems

7 problems · Systems of first-order linear differential equations and matrix exponentials.

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Ex.765A diagonalizable system

#diagonalization #eigenvalues #eigenvectors

Ex.766A system with three distinct eigenvalues

#eigenvalues #eigenvectors #general solution

Ex.767Derivative of the matrix exponential

#matrix exponential #derivative #series

Ex.768Properties of the matrix exponential

#matrix exponential #commuting matrices #derivative

Ex.1494Complex eigenvalues

#complex eigenvalues #real solutions #coefficients ind�termin�s

Ex.1495Matrix exponential with a nilpotent part

#matrix exponential #nilpotent #Jordan form

Ex.1496A linear system with a second member

#second member #variation of constants #matrix exponential