JSFHrestart; with(LinearAlgebra):Solution of an ODE with the following matrix (Ex. 1.7.3 (a)): A := < < 1, 1, 0, 0, 1> | <1, 0, 0, 0, -1> | <0, 0, 1, 0, 0> | <1, 0, 1, 1, 0> | < 1, 1, 0, 0, 1> >;B := A - Transpose(A);(L,E) := Eigenvectors(B);JordanForm(B);Maple's function returns the complexified diagonal matrix.If we want to obtain a block-diagonal real-valued matrix, we need to do this by hand.Note that the eigenvalues and the eigenvectors may be returned in a different order, and this needs to be accounted for by adjusting the indices below.v1 := E(1..5,1);v2 := map(Re,E(1..5,2)); v3 := map(Im,E(1..5,2));v4 := map(Re,E(1..5,4)); v5 := map(Im,E(1..5,4));P := < v1 | v2 | v3 | v4 | v5 >;Here is our Jordan form with diagonal block corresponding to the complex eignevalues.J := P^(-1) . B . P;JSFHTTdSMApJPFJUQUJMRV9TQVZFLzE0MDI4NjcyNDA5NjQ0OFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzoiJiImIiIiRiciIiFGKEYnRidGKEYoRighIiJGKEYoRidGKEYoRidGKEYnRidGKEYnRidGKEYoRidGJg==TTdSMApJPFJUQUJMRV9TQVZFLzE0MDI4NjcyNDA5NzQwOFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzoiJiImIiIhRidGJyEiIkYnRidGJ0YnRichIiNGJ0YnRidGKEYnIiIiRidGKkYnRidGJyIiI0YnRidGJ0YmTTdSMApJPFJUQUJMRV9TQVZFLzE0MDI4NjcyNDA4MDkyMFgqJSphbGdlYnJhaWNHNiI2IltnbCEjJSEhISImIiYiIiEqJl4jIiIiRioiIiMjRipGKyomXiMhIiJGKkYrRixeI0YrXiMhIiNGJg==TTdSMApJPFJUQUJMRV9TQVZFLzE0MDI4NjcyNDA4MTA0MFgsJSphbGdlYnJhaWNHNiI2IltnbCEiJSEhISM6IiYiJiEiIiIiISIiIkYoRigqJl4jI0YnIiIjRilGLSNGKUYtRihGKkYpRigqJl4jRi5GKUYtRi5GKEYvRilGKEYoXiNGJ0YoRihGKUYoXiNGKUYoRihGKUYmTTdSMApJPFJUQUJMRV9TQVZFLzE0MDI4NjcyNDA4Mjg0MFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzoiJiImIiIhRidGJ0YnRidGJ14jISIjRidGJ0YnRidGJ14jIiIjRidGJ0YnRidGJyomXiMhIiIiIiJGKyNGL0YrRidGJ0YnRidGJyomXiNGL0YvRitGMEYmTTdSMApJPFJUQUJMRV9TQVZFLzE0MDI4NjY1NTgwMDAzMlgqJSphbGdlYnJhaWNHNiI2IltnbCEjJSEhISImIiYhIiIiIiEiIiJGKEYoRiY=TTdSMApJPFJUQUJMRV9TQVZFLzE0MDI4NjcyNDA4MzkyMFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiYiJiIiIUYnRiciIiJGJ0YmTTdSMApJPFJUQUJMRV9TQVZFLzE0MDI4NjcyNDA4NDE2MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiYiJiwkKiQiIiMjIiIiRikjISIiRikiIiFGJ0YuRi5GJg==TTdSMApJPFJUQUJMRV9TQVZFLzE0MDI4NjcyNDA4NDQwMFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiYiJiIiIUYnRidGJyIiIkYmTTdSMApJPFJUQUJMRV9TQVZFLzE0MDI4NjcyNDA4NDY0MFgqJSlhbnl0aGluZ0c2IjYiW2dsISMlISEhIiYiJiIiISEiIkYnRidGJ0YmTTdSMApJPFJUQUJMRV9TQVZFLzE0MDI4NjcyNDA4NDc2MFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzoiJiImISIiIiIhIiIiRihGKEYoRihGKEYpRigsJCokIiIjI0YpRiwjRidGLEYoRipGKEYoRihGKEYoRihGKUYoRidGKEYoRihGJg==TTdSMApJPFJUQUJMRV9TQVZFLzE0MDI4NjcyNDA4OTQ0MFgsJSlhbnl0aGluZ0c2IjYiW2dsISIlISEhIzoiJiImIiIhRidGJ0YnRidGJ0YnLCQqJCIiIyMiIiJGKiEiIkYnRidGJ0YpRidGJ0YnRidGJ0YnRichIiNGJ0YnRidGKkYnRiY=