- Closed-book
- To be handed out Thursday, February 14 and due Tuesday,
February 19 at class time
- Time limit: 60 minutes, which should be more than you need
unless you hit a snag doing row reduction
- Calculators to be used only for number arithmetic, not for
anything else
- Covers HWKs 1-4.
- Covers Sections 1.1 - 1.5. plus the first part of 1.6 (through
the middle of page 62)
- Covers/includes
- elementary row operations and using them to find the
reduced row-echelon form for a given matrix
- solving systems of linear equations by using either
row-echelon form or reduced row-echelon form for the augmented
matrix (know how to do both); so using row operations with or
without back substitution
- terminology relating to systems of linear equations:
augmented matrix, coefficient matrix, consistent system,
inconsistent system, equivalent systems, etc
- terminology relating to homogeneous linear systems:
homogeneous system, trivial solution, nontrivial solution
- theorems describing possible solution set for a general
linear system, solution set for a homogeneous system
- where relevant, writing solution set (for a linear system)
in parametric form
- recognizing linear systems that are inconsistent
- matrix addition, forming scalar multiple of a matrix,
matrix multiplication, and rules/properties of matrix
arithmetic
- expressing Ax as a linear combination of the columns
of A
- zero matrix, identity matrix and their properties
- inverse matrices (what they are and how to find them, when
they exist)
- elementary matrices (what they are and what they
accomplish; how to see that they're always invertible; how to
find their inverses)
- transpose of a matrix and various properties of
transposes
- trace of a square matrix
- cancellation law for matrix multiplication does not hold in
general, does hold if the common factor is invertible
- inverse of a product
- transpose of a product
- transpose of an inverse (or inverse of a transpose of a
square matrix)
- formula for inverse of a 2 x 2 matrix
- matrix polynomials and associated notation
- the long theorem listing equivalent properties of a square
matrix (Thms 1.5.3 p52, 1.6.4 p61)
- using the notation A =
[aij]mxn
- writing an invertible matrix (or its inverse) as a product
of elementary matrices
- know Thm 1.6.1 (p59) but you don't need to know the proof
given there
- understand why A invertible ==> for each b,
Ax=b has a unique solution (Thm 1.6.2 p59)
- in particular, understand why A invertible ==>
Ax=0 has only the trivial solution
- understand why A being a product of elementary matrices
makes A invertible
- May include questions like the True-False questions in the
text
- May include questions that that ask you to provide examples
(or decide True-False and give counterexample if false)
- No proofs as such, for this quiz
- Suggested practice problems from the text. Don't do them all!
Remember that some questions make good review questions but not
good quiz/test questions.
- 1.1 p6: 3, 12, 13
- 1.2 p19: 3, 4, 5, 8, 9, 12, 16, 17, 28, 31, 32
- 1.3 p33: 1, perhaps some parts from 2-6, 7, 8, 11, 13, 14,
21, 22, 24, 27, 28, 29, 30
- 1.4 p47: perhaps some parts from 1-6, 7, 9, 11 or 12, 13,
15, 16, 17, 20, 29, 31, 32, 33, 35
- 1.5 p56: 2, 3, 4, 5, parts from 5-7, 8, 9,10, 11, 12, 18,
19, 20
- 1.6 p64: 1, 3, 9, 11, 22
Questions?
Come see me, or send
me e-mail or post in the Q&A conference in our FirstClass
conference MATH206-S01. When applicable, give page or section number,
give problem number, and be specific.
Go back to the top
- Alexia Sontag,
Mathematics
- Wellesley College
- Date Created: January 4, 2001
- Last Modified: February 11, 2002
- Expires: June 30, 2002