Reference:Peter J. Olver and Chehrzad Shakiban, Applied Linear Algebra, 2 nd edition, Springer, 2018.

Course: MAT3341 Applied Linear Algebra. University of Ottawa

Exercise:

Recall that we define the exponential of a matrix squaree A byeA=k=0(1/k!)Ak I) Demonstrate that if v is a proper vector of A associated with the eigenvalue then v is a eigenvector of e^A associated with the eigenvalue e.

Ii) Use the definition (1) to calculate e^tB for t R andB=000100320 Iii) Let x(t) be the solution of the problem at the initial value x = Bx, x(0) = x₀. Give all the initial conditions x₀ R³ for which x(t)₂remains bounded when t .