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Exercise:
Find the eigenvalues and eigenvectors for the following matrices: abcliste abc A leftmatrix- & & -matrixright abc B leftmatrix & - & matrixright abc C leftmatrix- & - & matrixright abc D leftmatrix- & - & matrixright abc E leftmatrix & - - & matrixright abc F leftmatrix & & & & & & matrixright abc G leftmatrix- & - & - & & & & matrixright abcliste

Solution:
Remark: The eigenvectors are only defined up to an arbitrary scalar factor. abcliste abc Eigenvalues lambda_ - and lambda_ - with eigenvectors bf v_ leftmatrix matrixright bf v_ leftmatrix matrixright abc Eigenvalues lambda_ -i and lambda_ i with eigenvectors bf v_ leftmatrixi matrixright bf v_ leftmatrix-i matrixright abc Eigenvalues lambda_ -frac+sqrt and lambda_ -frac-sqrt with eigenvectors bf v_ leftmatrixfrac+sqrt matrixright bf v_ leftmatrixfrac-sqrt matrixright abc Eigenvalues lambda_ -frac+sqrti and lambda_ -frac-sqrti with eigenvectors bf v_ leftmatrixfrac+sqrti matrixright bf v_ leftmatrixfrac-sqrti matrixright abc Eigenvalues lambda_ and lambda_ with eigenvectors bf v_ leftmatrix/ matrixright bf v_ leftmatrix- matrixright abc Eigenvalues lambda_ lambda_ and lambda_ with eigenvectors bf v_ leftmatrix - matrixright bf v_ leftmatrix -/ matrixright bf v_ leftmatrix matrixright abc Eigenvalues lambda_ - lambda_ and lambda_ with eigenvectors bf v_ leftmatrix- - matrixright bf v_ leftmatrix - matrixright bf v_ leftmatrix / / matrixright abcliste
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Exercise:
Find the eigenvalues and eigenvectors for the following matrices: abcliste abc A leftmatrix- & & -matrixright abc B leftmatrix & - & matrixright abc C leftmatrix- & - & matrixright abc D leftmatrix- & - & matrixright abc E leftmatrix & - - & matrixright abc F leftmatrix & & & & & & matrixright abc G leftmatrix- & - & - & & & & matrixright abcliste

Solution:
Remark: The eigenvectors are only defined up to an arbitrary scalar factor. abcliste abc Eigenvalues lambda_ - and lambda_ - with eigenvectors bf v_ leftmatrix matrixright bf v_ leftmatrix matrixright abc Eigenvalues lambda_ -i and lambda_ i with eigenvectors bf v_ leftmatrixi matrixright bf v_ leftmatrix-i matrixright abc Eigenvalues lambda_ -frac+sqrt and lambda_ -frac-sqrt with eigenvectors bf v_ leftmatrixfrac+sqrt matrixright bf v_ leftmatrixfrac-sqrt matrixright abc Eigenvalues lambda_ -frac+sqrti and lambda_ -frac-sqrti with eigenvectors bf v_ leftmatrixfrac+sqrti matrixright bf v_ leftmatrixfrac-sqrti matrixright abc Eigenvalues lambda_ and lambda_ with eigenvectors bf v_ leftmatrix/ matrixright bf v_ leftmatrix- matrixright abc Eigenvalues lambda_ lambda_ and lambda_ with eigenvectors bf v_ leftmatrix - matrixright bf v_ leftmatrix -/ matrixright bf v_ leftmatrix matrixright abc Eigenvalues lambda_ - lambda_ and lambda_ with eigenvectors bf v_ leftmatrix- - matrixright bf v_ leftmatrix - matrixright bf v_ leftmatrix / / matrixright abcliste
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Differential equations
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eigenvalue, eigenvector, linear algebra, matrix
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ENG (English)
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Calculative / Quantity
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