MATH 331 FINAL EXAM REVIEW
Here is a review sheet for your upcoming nal exam. Remember that the nal exam will
be cumulative to the beginning of the quarter. Enjoy!
(1) Section 4.3: Linear Independence and Bases. This section discussed the notion of
linear
MATH 331 MIDTERM SOLUTIONS
Here are the solutions to you recent exam. Enjoy!
(1) (a) The matrix is
.
. 11
.
.
. 4
.
.
011.4
.
122
2 0 1
(b) By preforming the row operations r2 r2 2r1 , followed by r3 4r3 + r2 ,
we get the row reduced matrix
.
12
2 . 11
.
MATH 331 MIDTERM REVIEW SHEET
Hi everyone, here is a review sheet for your midterm. Remember that the midterm will
cover those sections that the quiz did, in addition to those reviewed below.
(1) Section 1.4: The matrix equation Ax = b. This section revie
MATH 331 QUIZ # 1 REVIEW SHEET
Hi kids! Here is your review sheet for your rst quiz of Math 331. The following sections
will be covered. Good luck!
(1) Section 1.1: Systems of Linear Equations. This section introduces the augmented
coecient matrix of a li
MATH 331 QUIZ # 1 SOLUTIONS
Hi everyone! Here are the solutions to the rst
(1) (a) The matrix is as follows:
.
134.
.
.
.
0 1 1 .
.
801.
.
quiz. Enjoy!
3
0
6
(b) Using the row operations, we get the following. The row operations r3
r3 8r1 , then r3 r3 +
MATH 331 QUIZ # 2 SOLUTIONS
Hi kids! Here are the solutions to the recent Quiz # 2. Enjoy!
(1) (a) By preforming row operations, we nd the that (unique) reduced row-echelon form of
A is
1 2 0 10 0
A 0 0 1 1 0 .
000 0 1
Thus, the solution (x1 , x2 , x3 , x
MATH 331 QUIZ # 2 REVIEW SHEET
Hi everyone, here is a review sheet for your upcoming quiz. It will cover the sections
listed below (the nal exam will be cumulative to the beginning of the quarter). Enjoy!
(1) Section 2.2: The inverse of a matrix. The big