la_FE_study_guide

# la_FE_study_guide - orthogonal projection of b on W = col(A...

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STUDY GUIDE FOR MAS 2103 FINAL EXAM Be able to do each of the following: 1. Find the inner product, norm and distance. 2. Find the solution of the homogeneous system A ! x = ! 0; use Gauss elimination on [ A | ! 0] to obtain a row echelon form [ G | ! 0] and use back-substitution to find the solution ! x . 3. Identify which columns of G are leading columns, which columns of G are non- leading columns, and which columns will give the free variables in the solution of the system. 4. Find a basis for and the dimension of the null(A), col(A), and row(A). 5. Use the Gram-Schmidt method to construct an orthogonal basis from the basis vectors. 6. Find the least-square solution by solving the associated normal system and the
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Unformatted text preview: orthogonal projection of ! b on W = col(A). 7. Solve the eigenvalue problem A ! x = ! ! x for the eigenvalues and corresponding eigenvectors. 8. Each eigenvalue has an eigenspace. Find a basis for each eigenspace. 9. State the algebraic multiplicity and geometric multiplicity for each eigenvalue. 10. Let AP = PD for the symmetric matrix A and P. Show that P is an orthogonal matrix. 11. Find the eigenvalues of A by solving AP = PD for the diagonal matrix D; show that A = PDP T . 12. Compute the Wronskian and show that S is a linearly independent set of vectors....
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