# Previous answers holtlinalg1 61015 find a basis for

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A=,λ=410 96 5..
4.1/1 points |Previous AnswersHoltLinAlg1 6.1.015.Find a basis for the eigenspace ofAassociated with the given eigenvalueλ141[1;4;1]A=,λ=94 1281884 13.5...
Consider the matrixAFind the characteristic polynomial for the matrixA. (Write your answer in terms ofλFind the real eigenvalues for the matrixA. (Enter your answers as a comma-separated list.)λ=Find a basis for each eigenspace for the matrixAA=42015..).-41[-4;1](smaller eigenvalue)51[5;1](larger eigenvalue)59.:00
Consider the matrixAFind the characteristic polynomial for the matrixA. (Write your answer in terms ofλFind the real eigenvalues for the matrixA. (Enter your answers as a comma-separated list.)λ=Find a basis for each eigenspace for the matrixAEigenspace ofA=4001302 31..).110[0;0;1](smallest eigenvalue)04/31[0;4/3;1]551[5;5;1](largest eigenvalue)Solution or ExplanationCharacteristic polynomial:Eigenvalues:det(AλI3) = detλ= det=(λ3)(λ4)(λ+ 1).4001302 311 0 00 1 00 0 14λ0013λ0231λ(λ3)(λ4)(λ+ 1) = 0λ=3,λ=4, andλ=1.λ=3:
so a basis for this eigenspace isEigenspace ofso a basis for this eigenspace isEigenspace ofso a basis for this eigenspace isA3I3=~,1 001 002 341 000340 00.0143λ=4:A4I3=~,000110235110015000.551λ=1:A(1)I3=~,50 01402 3050 00400 0 0.001

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