For this assessment, you will develop an 8–14 slide PowerPoint presentation with thorough speaker's notes designed for a hypothetical in-service session related to the improvement plan you developed in Assessment 2.

[ANSWER] MAT350 6.2 MATLAB: Eigenvalues and Eigenvectors

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MAT350 6.2 MATLAB: Eigenvalues and Eigenvectors

In this activity you will find the eigenvalues and eigenvectors of a square matrix.

Consider the following matrix.

A = [3 1 0; 0 3 1; 0 0 3]

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MAT350 6.2 MATLAB: Eigenvalues and Eigenvectors

In this activity you will find the eigenvalues and eigenvectors of a square matrix.

Consider the following matrix.

A = [3 1 0; 0 3 1; 0 0 3]

 

Use the command poly() to find the characteristic polynomial.

CharacteristicPoly = poly(A)

 

Use the command roots() to find the eigenvalues.

eigenvalues = roots(CharacteristicPoly)

The eig() command returns diagonal matrix D of eigenvalues and matrix V whose columns are the corresponding eigenvectors.  For example, the value on the diagional in the first column of D is the eigenvalue associated with the eigenvector in the first column of V. 

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The eigenvectors in V are normalized, each having a magnitude of 1.

[V, D] = eig(A)

Use the following matrix C for this activity.

6  3 8

C = [ 0 -2 0 ]

1  0 -3

Enter the matrix C.

C = [6 3 -8; 0 -2 0; 1 0 -3]

Find the coefficients of the characteristic polynomial.  Store them in PolyCoeffs.

PolyCoeffs = poly(C)

Use the command roots() to find the eigenvalues.  Store them in evals.

evals = roots(PolyCoeffs)

Use the eig() command.  Store the eigenvalues in matrix eigDiag.  Store the associated

eigenvectors in eigV.

[eigV, eigDiag] = eig(C)

Related; MAT350 5.8 MATLAB: Change of Bases.

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