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QUESTION
prove that if A is an real n x n matrix, and Aa = 0 (A a matrix, a a vector, 0 a vector) then the matrix e^(tA) satisfies e^(tA)*a = a for all t in R...
prove that if A is an real n x n matrix, and Aa = 0 (A a matrix, a a vector, 0 a vector)then the matrix e^(tA) satisfies e^(tA)*a = a for all t in R
Aa = 0∞ (1) ke tA =tk A!This is an n × n matrixkk=0∞∞kk −1e tA a =tk A! a =tk Ak! Aa + Iakk=0k=1 As Aa = 0e tA a = I a = a ∀ t ∈ R 1