Linear Algebra [pdf answers]
Jim HefferonCourse website
Linear algebra II focuses on linear maps. We will revisit the fact that every linear map has a matrix representation. As a result, the range and the null space of a linear map are corresponding to the column space and the null space of a matrix. Therefore, almost everything we are going to learn in this course can be written in the matrix form. The second goal of this course is to learn how to diagonalize a matrix. To achieve this, we generalize the definition of the determinant of a 2 by 2 matrix to a square matrix of any order. Then you are going to know how to calculate the characteristic polynomial and to diagonalize a matrix. Matrix diagonalization is an important technique that has plenty of applications. For example, diagonalization allows you to compute the power of a matrix systematically, to rotate an ellipse to nice coordinates, to solve a linear system of differential equations, and so on. If possible, we will also learn how to use Sage, a mathematics software, to do these tedious computations we mentioned.
3*5% Quizzes + 25% Midterm1 + 30% Midterm2 + 30% Final exam + extra 5% participation
You get 0.5 participation point whenever you ask a question, correct a mistake, or share your thoughts in the class. The maximum participation point is 5 points for each person. Record your activities using the link above.
No homework. Sample questions will be posted weekly for you to prepare the exams.
The question type of each quiz will be given but the numbers will be different. No partial credits for quizzes. However, within the two weeks (and before the final exam) after a quiz is given, you may ask for extra tests of the same question type. Your score for a quiz is the average of all tests you have taken under the same question type. Note: If you missed the quiz in class, that counts as a zero.
For example, you missed Quiz 1 in class, and you asked for 3 extra tests and get 2 of them correct, then your score for Quiz 1 is (0 + 5 + 5 + 0) / 4 = 2.5.
Here are the Kahoot! quizzes we played in the class.
Students with diverse learning styles and needs are welcome in this course. In particular, if you have a disability/health consideration that may require accommodations, please feel free to approach me.
Percentage scores will be converted to letter grades according to the university-wide standard table.
You are expected to attend the classes.
If you miss some course components due to illness, accident, family affliction, or religious observances, please talk to me and provide the documentation. In such cases, the course component is excused, and your course score will be calculated by distributing the weight of the missed item(s) across the other course components. Missing components are limited to at most 20%.
