71 Eigenvalues and Eigenvectors Eigenvalues and Eigenvectors The Characteristic

# 71 eigenvalues and eigenvectors eigenvalues and

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§7.1Eigenvalues andEigenvectorsEigenvalues andEigenvectorsThe CharacteristicPolynomialFinding EigenvectorsImportantINotice that we had to row reduce a completely differentsingular matrix for each eigenvalue.IAt no time, did we row reduce the original matrixA.
§7.1Eigenvalues andEigenvectorsEigenvalues andEigenvectorsThe CharacteristicPolynomialFinding EigenvectorsImportantINotice that we had to row reduce a completely differentsingular matrix for each eigenvalue.IAt no time, did we row reduce the original matrixA. Weshould NEVER have to row reduceAitself at all to findeigenvalues or eigenvectors.
§7.1Eigenvalues andEigenvectorsEigenvalues andEigenvectorsThe CharacteristicPolynomialFinding EigenvectorsImportantINotice that we had to row reduce a completely differentsingular matrix for each eigenvalue.IAt no time, did we row reduce the original matrixA. Weshould NEVER have to row reduceAitself at all to findeigenvalues or eigenvectors. Row reducingAin an effort to“simplify” the work will throw the answer off.
§7.1Eigenvalues andEigenvectorsEigenvalues andEigenvectorsThe CharacteristicPolynomialFinding EigenvectorsImportantINotice that we had to row reduce a completely differentsingular matrix for each eigenvalue.IAt no time, did we row reduce the original matrixA. Weshould NEVER have to row reduceAitself at all to findeigenvalues or eigenvectors. Row reducingAin an effort to“simplify” the work will throw the answer off. Rowequivalent matrices DO NOT share eigenvalues andeigenvectors.
§7.1Eigenvalues andEigenvectorsEigenvalues andEigenvectorsThe CharacteristicPolynomialFinding EigenvectorsImportantINotice that we had to row reduce a completely differentsingular matrix for each eigenvalue.IAt no time, did we row reduce the original matrixA. Weshould NEVER have to row reduceAitself at all to findeigenvalues or eigenvectors. Row reducingAin an effort to“simplify” the work will throw the answer off. Rowequivalent matrices DO NOT share eigenvalues andeigenvectors.IThe matrix we end up row reducingλIn-Awill ALWAYSend up being singular.
§7.1Eigenvalues andEigenvectorsEigenvalues andEigenvectorsThe CharacteristicPolynomialFinding EigenvectorsImportantINotice that we had to row reduce a completely differentsingular matrix for each eigenvalue.IAt no time, did we row reduce the original matrixA. Weshould NEVER have to row reduceAitself at all to findeigenvalues or eigenvectors. Row reducingAin an effort to“simplify” the work will throw the answer off. Rowequivalent matrices DO NOT share eigenvalues andeigenvectors.IThe matrix we end up row reducingλIn-Awill ALWAYSend up being singular. That is, the system(λIn-A)x=0will always have (infinitely many) nontrivial solutions.
§7.1Eigenvalues andEigenvectorsEigenvalues andEigenvectorsThe CharacteristicPolynomialFinding EigenvectorsImportantINotice that we had to row reduce a completely different