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Math 214 Spring 2008: Quizzes |
| Quiz | Topic | Hint | Assigned | Due |
| BONUS 7 | Orthogonal Matrices | The main condition that defines an orthogonal matrix is that Q-1 = QT.(when Q is square). The more general condition is that QTQ = I. | 4/11 | 4/14 |
| NINE | 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? Recall that you only know how to project a vector onto another vector, not onto a multi-dimensional subspace. | 4/11 | 4/14 |
| BONUS 6 | Diagonalization! | More practice with diagonalization, eigenvectors and eigenvalues. Recall the conditions for when a matrix is diagonalizable. (i.e. S must have n distinct eigenvectors, but not neccessarily n distinct eigenvalues). | 4/4 | 4/7 |
| EIGHT | 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. | 4/4 | 4/7 |
| BONUS 5 | 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. HINT: think about the restrictions on the eigenvalues of a matrix. Are there any? How would the eigenvalues and eigenvectors of a matrix change if one swapped the rows and columns? |
3/28 | 3/31 |
| 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? | 3/28 | 3/31 |
| BONUS 4 | Rank, Independence, Basis and Dimension | This quiz helps with collecting all the various concepts surrounding rank, linear independence, basis, subspaces and dimension together. | 3/7 | 3/17 |
| 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. | 3/7 | 3/17 |
| FIVE | TRUE OR FALSE: Matrix Inverses | 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 | 2/22 | 2/25 |
| BONUS 3 | TRUE OR FALSE. | To get full credit for a TRUE answer you have to PROVE that the statement is TRUE. | 2/22 | 2/25 |
| FOUR | Matrix Operations | Think carefully about what kind of matrices can self-multiply and what it means for a matrix to be equal to another. YOUR EXPLANATION OF "WHY" IS WORTH MORE THAN YES OR NO. | 2/15 | 2/20 |
| 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 (in space). | 2/8 | 2/11 |
| GROUP 1 | Reduced Row Echelon Form | The main thing to think about is how the different forms of the reduced row echelon form correspond to the different kinds of linear systems that have 0, 1 or Infinite number of solutions | 2/13 | 2/13 |
| 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. | 2/8 | 2/11 |
| 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.. | 2/1 | 2/4 |
| TWO | Solving Linear Systems | Think carefully about all the possible values of a and how that may influence what calculations you can make. | 2/1 | 2/4 |
| ONE | Vectors and Projections | Draw a picture of the two projections (u upon v and v upon u) and see if you think they would be equivalent or not. |
1/25 | 1/28 |
To obtain solutions of Quizzes, click on the Quiz #.
Last Updated April 16, 2008