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 6.5 MATLAB: Diagonalization

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MAT350 6.5 MATLAB: Diagonalization

In this activity you will find the matrix P that diagonalizes a given matrix and the resulting diagonal matrix D, and utilize these to indirectly find a higher power of the given matrix.

Consider the matrix A.

A = [ 1 1 ]

-2 4

Higher powers of A can be found indirectly using the diagonalization matrix P and resulting diagonal matrix D.  These matrices were found using the eig() command in zyLab 6.2.  The matrix A to the kth power can be indirectly calculated by.

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MAT350 6.5 MATLAB: Diagonalization

In this activity you will find the matrix P that diagonalizes a given matrix and the resulting diagonal matrix D, and utilize these to indirectly find a higher power of the given matrix.

Consider the matrix A.

A = [ 1 1 ]

-2 4

Higher powers of A can be found indirectly using the diagonalization matrix P and resulting diagonal matrix D.  These matrices were found using the eig() command in zyLab 6.2.  The matrix A to the kth power can be indirectly calculated by.

A = [1 1; -2 4]

[P, D] = eig(A)

Indirectly find A^5 using P and D.  The command power(D,5) raises every element in the diagonal matrix D

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to the fifth power.

A5indirectly = P*power(D,5)*inv(P)

The same result can be found directly, but the direct method is not computationally practical for higher powers.

A5directly = A^5

Use the following matrix for this activity.

1 2 2

C = [ 2 1 2 ]

2 2 1

Enter matrix C.

C = [1 2 2; 2 1 2; 2 2 1]

Use the eig() command to find the matrix P that diagonalizes C and the resulting diagonal matrix D.  Store these in P and D, respectively.

[P, D] = eig(C)

Indirectly find C^4, using P and D, and using the power() command on D.  Store the result in C4.

C4 = P * power(D,4) * inv(P)

Also read; MAT350 6.2 MATLAB: Eigenvalues and Eigenvectors.

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