Midterm 1
Scheduled on 2/24 Tuesday.
The exam will be based on the materials corresponding to HW 1-- HW 5, which are on Ch 1 and Ch 2.
Practice Exams
Exam 1 Fall 2024 (its solution to be posted later; for now, work out the problems on your own) and its Solution
Exam 1 Fall 2025 (its solution to be posted later; for now, work out the problems on your own) and its Solution
Do NOT assume the upcoming exam this semester will have (almost) the identical questions.
You must practice more problems if aiming an A or a B.
2/14 Update
Fall 24 & Fall25 topics were covered in a slightly different order and more proofs compared to the current semester. The following adjustments are needed accordingly.
The upcoming midterm 1 in Spring 26 will ask fewer proof questions (but you will surely see at least one); some of the proof questions in my old exam may be asked as True/False or short answers.
The following questions were not on the two old exams above. Be sure to study
HW 1.3 Matrix Multiplication: Columns and Rows: "1.3 Class exercise: Rows and Columns of AB" on the last page
HW 1.3 Matrix Equation, Linear System, and Linear Combination (Def): "1.3 Class exercise: Ax in Linear Combination of Column vectors" on the last page
HW Exercises 1.6: #14(see Example 3 on pp.8-9 in 1.6 Non-homogeneous Ax=b, Invertible matrix TFAE (e)(f).
Do (a)--(d) as in the lecture file), that is
(a) Rewrite the given linear system in a matrix equation
(b) Find the conditions on the b_i's for the system to be consistent, as asked in the exercise
(c) Integrate the conditions on the b_i's found in (b) to rewrite the solution b in column vector in independent variable(s); be sure to give the range of the independent variable(s)
(d) What can you say about the invertibility of A?
2/16 Update
No homework due on the exam date
2/20 Update
Links to the solutions of my old exams have been posted above, next to each exam.
Exam information and updates will appear below until the actual exam date.