# we can enter a matrix into Maple in several ways # the following way enters the matrix by specifying the columns A := <<1, 1>|<1, 0>>; # The following way enters the matrix by specifying the rows with(LinearAlgebra): A := Matrix([[1,1], [1, 0]]); # You multiply matrices using a period for the # multiplication symbol. That tells Maple that # you want to do matrix multiplication rather # than entry-wise multiplication. A.A; # You can also take an arbitrary power of a matrix: with(LinearAlgebra): MatrixPower(A, 5); # You can use this to find the long-run dynamics # with any initial population size vector, X with(LinearAlgebra): X := <1, 0>; MatrixPower(A, 10).X; #You can find the largest eigenvalue of A using #code like: with(LinearAlgebra): phi := Eigenvalues(A)[1] # You should find that phi := (1 + sqrt(5))/2; # You can compute the long-run frequencies in each # strata with code like: with(LinearAlgebra): W := evalf(MatrixPower(A, 5).X/(phi^5)); W := W/(W[1]+W[2]); # You can compute the eigenvectors with code like: with(LinearAlgebra): E := Eigenvectors(A, output='vectors'); evalf(E[1..2, 1]/(E[1,1] + E[2,1]));