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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

This note was uploaded on 10/18/2011 for the course MAS 2103 taught by Professor Shaw during the Summer '11 term at Valencia.

Ask a homework question - tutors are online