Question

To find eigenvalues and eigenvectors in Maple, use the following instructions. with(LinearAlgebra); to bring in the necessary routines A:=<<2,0>|<-3,5>> to store the matrix A = (2 -3, 0 5) v,e:=Eigenvectors(A); to produce v, e -> (2, 5) (1 -1, 0 1), where v contains the eigenvalues of A and the matrix e has the eigenvectors as its columns The corresponding instructions in Mathematica are as follows. A={{2,0},{-3,5}} {vals,vecs}=Eigensystem[A] The output of this instruction is {{2,5},{{1,0},{-1,1}}}. Use technology to find the eigenvalues and eigenvectors of the matrix H. In each case, try to obtain eigenvectors with integer coefficients. H = (3 0 0, 1 3 -2, 1 0 1) One of the eigenvalues of H has algebraic multiplicity 2; that is, it appears as a double root of the characteristic polynomial. It may have two linearly independent eigenvectors, or only one. Which seems to be the case here? (Order eigenvalues from smallest to largest real part, then by imaginary part. For repeated eigenvalues, list the eigenvalue once and give a maximal set of linearly independent eigenvectors.)

          To find eigenvalues and eigenvectors in Maple, use the following instructions.

with(LinearAlgebra); to bring in the necessary routines
A:=<<2,0>|<-3,5>> to store the matrix A = (2 -3, 0 5)
v,e:=Eigenvectors(A); to produce v, e -> (2, 5) (1 -1, 0 1), where v contains the eigenvalues of A and the matrix e has the eigenvectors as its columns

The corresponding instructions in Mathematica are as follows.

A={{2,0},{-3,5}}
{vals,vecs}=Eigensystem[A]

The output of this instruction is {{2,5},{{1,0},{-1,1}}}.

Use technology to find the eigenvalues and eigenvectors of the matrix H. In each case, try to obtain eigenvectors with integer coefficients.

H = (3 0 0, 1 3 -2, 1 0 1)

One of the eigenvalues of H has algebraic multiplicity 2; that is, it appears as a double root of the characteristic polynomial. It may have two linearly independent eigenvectors, or only one. Which seems to be the case here? (Order eigenvalues from smallest to largest real part, then by imaginary part. For repeated eigenvalues, list the eigenvalue once and give a maximal set of linearly independent eigenvectors.)

To find eigenvalues and eigenvectors in Maple, use the following instructions.

with(LinearAlgebra); to bring in the necessary routines
A:=<<2,0>|<-3,5>> to store the matrix A = (2 -3, 0 5)
v,e:=Eigenvectors(A); to produce v, e -> (2, 5) (1 -1, 0 1), where v contains the eigenvalues of A and the matrix e has the eigenvectors as its columns

The corresponding instructions in Mathematica are as follows.

A=2,0,-3,5
vals,vecs=Eigensystem[A]

The output of this instruction is 2,5,1,0,-1,1.

Use technology to find the eigenvalues and eigenvectors of the matrix H. In each case, try to obtain eigenvectors with integer coefficients.

H = (3 0 0, 1 3 -2, 1 0 1)

One of the eigenvalues of H has algebraic multiplicity 2; that is, it appears as a double root of the characteristic polynomial. It may have two linearly independent eigenvectors, or only one. Which seems to be the case here? (Order eigenvalues from smallest to largest real part, then by imaginary part. For repeated eigenvalues, list the eigenvalue once and give a maximal set of linearly independent eigenvectors.)

Added by Mariano A.

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