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matlab_mat_eigen
Course: MATH 410, Fall 2009School: Bethel VA
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and Eigenvalues Eigenvectors1 1. Try the following commands (a) digits(4) (b) A = sym([1,1; 0,1]) (c) E = eig(A) (d) [V,E] = eig(A) Find the eigenvalues and eigenvectors for this matrix by hand and interpret the output. 2. Input the symbolic matrix (use sym as above): B= and try the commands: (a) SE = eig(B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finds eigenvalues symbolically. (b)...
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and Eigenvalues Eigenvectors1
1. Try the following commands (a) digits(4) (b) A = sym([1,1; 0,1]) (c) E = eig(A) (d) [V,E] = eig(A) Find the eigenvalues and eigenvectors for this matrix by hand and interpret the output. 2. Input the symbolic matrix (use sym as above): B= and try the commands: (a) SE = eig(B) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Finds eigenvalues symbolically. (b) NE = eig(vpa(B)) . . . . . . . . . . . . . . . . . . . . vpa changes from symbolic to numeric. (c) [SV,SE] = eig(B) (d) [NV,NE] = eig(vpa(B)) 3. Create a matrix using the command: C = sym(hilb(5)) and repeat the process in the previous part. 4. What are your observations about symbolic numerical vs. computations from the last two parts? 5. Using complete sentences and standard mathematical notation, write a brief report. Show your hand calculations and answer all the questions.
In the first example students must consider multiplicities. The last part should lead to a discussion of the fact that polynomials of degree 5 or higher cannot in general be solved symbolically and so exact symbolic ...
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