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Let A 3100 000 1 2 4 8 0 3 5 003 a 3 marks...

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Algebra

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Let A 3100 000 1 2 4 8 0 3 5 003 a 3 marks The eigenvalues of A are 2 and X 3 Find a basis for the eigenspace E of A associated to the eigenvalue X 2 and a basis of the eigenspace E of A associated to the eigenvalue A 3 A basis for the eigenspace Eis BE 481 A basis for the eigenspace Es is b 2 marks State the algebraic multiplicity and the geometric multiplicity of each eigenvalue of A Algebraic multiplicity of A 2 alg 2 Geometric multiplicity of A 2 geo 2 Algebraic multiplicity of A 3 alg 3 Geometric multiplicity of 3 geo 3 Hint compute the characteristic polynomial CA A of A

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