- Below are some practice problems for the midterm, try to study till you feel comfortable with those
- Midterm 1 covers the first 3 Chapters (3.4 excluded)
- The midterm will take place in class, usual place and time. Make sure you arrive before 2:20pm. The exam will end at 3:40pm.
- No calculators, books and notes are allowed. If you have your book or notes with you, they should stay in a bag during the exam, not to be seen from outside.

Practice Problems (The exam will consist in five problems.)

- Exercise 1.2-9
- Exercise 1.2-30
- Exercise 1.3-32
- Exercise 1.3-46
- Exercise 2.2-23
- Exercise 2.2-30
- Exercise 2.3-47
- Exercise 2.3-57
- Exercise 2.4-31
- Exercise 2.4-41
- Exercise 3.1-23
- Exercise 3.2-46
- Exercise 3.2-49
- Exercise 3.3-26
- Exercise 3.3-31

Checklist for Midterm I

- Solve a system of linear equations using Gauss-Jordan elimination
- Reduced row-echelon form (rref) of a matrix, how to find it, and how the rref of a matrix gives the solution of a linear system
- What is the rank of a matrix?
- How does the solution of a linear system depend on the ranks of coefficient- and augmented matrices
- How to add and multiply matrices
- Matrix multiplication is associative, but not commutative!
- What is a vector? How to add vectors and take a scalar multiple of a vector? When two vectors are parallel?
- What is R
^{n}? What operations can one do with its elements? - Calculate the dot product of two
vectors in R
^{n}. - What does it mean that two vectors are orthogonal?
- What is a linear transformation? Can you give some examples?
- What is the matrix of a linear transformation and how to find it
- Linear transformations on a plane: scaling, projection, reflection, rotation.
- What is a composition of linear transformations and how to find its matrix
- What is the inverse thansformation?
- Inverse matrix, what is it? how to compute it?
- What is a subspace of R
^{n}? - What is a linear combination of vectors?
- What is a span of vectors?
- Which vectors are said to be linearly dependent?
- Which vectors are said to be linearly independent?
- How to test linear dependence/independence?
- What is the kernel of a linear transformation?
- What is the image of a linear transformation?
- Find basis of the kernel and image of a linear transformation.
- What does it mean that vectors form a basis of a subspace?
- What is the dimension of a subspace?
- Can you say "A matrix is invertible" in nine different ways?
- The rank of a matrix and the dimension of the image, how are they related?
- If T is a linear transformation then dim(ker(T))+dim(im(T))= ??