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Math 214 Spring 2007: Quiz |
| Quiz (soln) | Topic | Hint | Assigned | Due |
| BONUS 8 | Orthogonal Matrices | The main condition that defines an orthogonal matrix is that Q-1 = QT. This implies that QTQ = I. | 4/13 | 4/16 |
| TEN | Orthogonal Complements | Just keep in mind what vector is being projected in what direction, so that your answer should be a scalar multiple of exactly what vector? | 4/13 | 4/16 |
| BONUS 7 | Practice with Diagonalization | More practice with diagonalization. Recall the conditions for when a matrix is diagonalizable. | 4/6 | 4/9 |
| NINE | Applications of Similarity and Diagonalization | 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. Keep all the fractions around and THEN take the limit as n -> infinity. | 4/6 | 4/9 |
| BONUS 6 | Properties of Eigenvalues and 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. | 3/30 | 4/2 |
| EIGHT | Determinants | Think about how the determinant changes as the matrix changes. Relate the matrix you have (and its determinant) and compare to the matrix you're given. | 3/30 | 4/2 |
| SEVEN | Eigenvalues, Eigenvectors and Inverses | Practice finding the eigenvalues and eigenspaces associated with a given matrix (and its inverse). How might the eigenvalues of a matrix and its inverse be related? | 3/23 | 3/26 |
| BONUS 5 | Rank, Independence, Basis and Dimension | This quiz helps with collecting all the various concepts surrounding rank, linear independence, basis, subspaces and dimension together. | 3/9 | 3/19 |
| SIX | Subspaces Associated With Matrices | Think about the ways the rank of a system relates to the associated subspaces of a matrix and the implications that has for whether a solution will have a unique solution or not. | 3/9 | 3/19 |
| BONUS 4 | TRUE OR FALSE | To get full credit for a TRUE answer you have to PROVE that the statement is TRUE. | 2/23 | 2/28 |
| FIVE | TRUE or FALSE: Inverse Matrices | A statement is only TRUE if it always TRUE but it is FALSE if you can provide a COUNTER EXAMPLE which satisfies the hypothesis of the statement but not the conclusion. | 2/23 | 2/28 |
| BONUS 3 | Linear Independence and Linear Dependence | Recall that the definition of linear independence means that the only solution to Ax=0 is x=0. You could also use the Rank Theorem. | 2/16 | 2/21 |
| FOUR | Idempotent Matrices | Think carefully about what kind of matrices can self-multiply and what it means for a matrix to be equal to another. | 2/16 | 2/21 |
| BONUS 2 | Homogeneous and Non-homogeneous linear systems. | Look at the two vector forms of your solutions for the homogeneous case (a=b=0) and non-homogeneous case (a=b=1) and interpret how these geometric objects are related to each other. | 2/9 | 2/12 |
| THREE | Solving Linear Systems by Elimination | Think carefully about all the possible values of a and how that may influence what calculations you can make. | 2/9 | 2/12 |
| BONUS 1 | 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. | 2/2 | 2/5 |
| TWO | Solving Linear Systems | Think carefully about all the possible values of a and how that may influence what calculations you can make. | 2/2 | 2/5 |
| ONE | Vectors and Projections | Draw a picture of the two projections (u upon v and v upon u). |
1/26 | 1/29 |
Last Updated April 18, 2007