problems4.1 - Math 307: Problems for section 4.1 November...

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Math 307: Problems for section 4.1November 14, 20121.For the following matrices find(a) all eigenvalues(b) linearly independent eigenvectors for each eigenvalue(c) the algebraic and geometric multiplicity for each eigenvalueand state whether the matrix is diagonalizable.A=bracketleftbigg372-2bracketrightbigg(calculate by hand)B=1-3 33-5 36-6 4(calculate using Matlab/Octave or otherwise)C=12120-2-1 23(calculate using Matlab/Octave or otherwise)2.Find a3×3real, non-zero (i.e.not all entries zero) matrix which has all three eigenvalueszero.3.(a) By hand find a matrix with eigenvaluesλ1= 1andλ2= 2and corresponding eigen-vectorsv1=bracketleftbigg12bracketrightbiggv2=bracketleftbigg21bracketrightbigg(b) Using Matlab/Octave or otherwise, find a matrix with eigenvalues
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