| Resources | Term Project | ||||
| Exams | HW | ||||
| Syllabus | |||||
Math 214 Spring 2006: Quiz |
| Topic | Hint | Assigned | Due |
| Orthogonal Matrices | Recall that an orthogonal matrix Q must obey the relationship that QTQ=I. This should give you a system of solvable nonlinear equations for a, b and c. Consider all the cases. | 4/12 | 4/17 |
| Orthogonality | Recall the definition of and relationship between perpw(v) and projw(v) | 4/12 | 4/17 |
| Practice with Diagonalization | Look carefully at the cubic to see what atleast one root of it is and then factor it. There is a repeated eigenvalue. | 4/7 | 4/10 |
| Application of Similarity, Determinants and Diagonalization | det(ABC)=det(A)det(B)det(C) | 4/7 | 4/10 |
| Properties of Eigenvectors | TRUE or FALSE quiz. Recall to show something is TRUE, it must always be TRUE. For FALSE you just have to list a counter example and explain how this refutes the statement, | 3/24 | 3/27 |
| Application of Eigenvalues | Asymptotic behavior relates to behavior as some parameter gets infinitely large. It's interesting that we can do this for a matrix being raised to an asymptotic power. | 3/24 | 3/27 |
| Fun with determinants! | Think about how the determinant changes as the matrix changes. elate the matrix you have (and its determinant) and compare to the matrix you're given. | 3/24 | 3/27 |
| Eigenvalues and Eigenvectors | Practice finding the eigenvalues and eigenspaces associated with a given matrix (and its inverse). How much the eigenvalues of a matrix and its inverse be related? | 3/24 | 3/27 |
| Dimension, Span, Subspaces and Rank | Think about the many ways the rank and nullity relate to each other. | 3/10 | 3/20 |
| Subspaces Associated With Matrices | Practice finding the subspaces associated with a matrix from a linear system and the implications it has for the solutions of that system. | 3/10 | 3/20 |
| Inverse Matrices and Gauss Jordan elimination | Use Gauss-Jordan elimination to find the Inverse of A and then check your answer for a particular example. What are values of a and b in this example? | 2/24 | 2/27 |
| Inverse Matrices (True or False) | Consider all the equivalent statements in the
Fundamental Theorem of Invertible Matrices.
Recall that for a statement to be true it has to be true for all possible scenarios. |
2/24 | 2/27 |
| Linear Independence and Matrix Operations (True or False) | Recall that for a statement to be true it has to be true for all possible scenarios. | 2/17 | 2/22 |
| Idempotent Matrices | Think carefully about what it means for one matrix to be equal to another. | 2/17 | 2/22 |
| Span and Linear Independence | Consider the definition of linear independence and Theorem 2.6 | 2/10 | 2/13 |
| Solving Linear System Using Row Reduction | Think carefully about all the possible values of a and how that may influence what calculations you can make. | 2/10 | 2/13 |
| Solving Linear System by Elimination | Think carefully about all the possible values of a and how that may influence what calculations you can make. | 2/3 | 2/6 |
| Operations on Vectors and Matrices | Recall that a m by n matrix multiplied by a n by p matrix produces a m by p matrix. All vectors (row or column) are special cases of matrices. | 2/3 | 2/6 |
| Vectors and Projections | Draw a picture of the two different projections (u upon v and v upon u). |
1/27 | 1/30 |
| Lines and Planes | Note that a plane can be defined as the set of points orthogonal to a vector, so that Ax + By + Cz = D has [A,B,C] as its normal vector. Thus you can find the angle between a line and a plane by finding the angle between the line's direction vector and the plane's normal vector. | 1/27 | 1/30 |
Last Updated January 22, 2007