Department of Mathematics
Fall 2013, MATH 369
Colorado State University
Homework Assignment I
Due Sep 9, 2013
1. Find the point of intersection of the planes 4x 2y + z = 0, x 3y + z = 5 and 6x + 2y 11z = 7.
Solution. To nd the intersection we will solve a
Practice Problems for Exam 1
NOTE: These problems do not cover EVERYTHING.
Part A - Calculator Allowed
1. Equation of plane in 4D. Goes through 4 coordinate points. Distance
from a point (not on the plane) to the plane.
2. Given the matrix A below, using
Name:
SI:
Exam 2, Math 369
October 24, 2012
Part A
1. Let M1 , M2 , M3 and M be given below. (Suggestion: Read both problems to be solved. Much of the work can be simultaneously.)
(a) Show that the set cfw_M1 , M2 , M3 is linearly independent.
(b) Find t
Practice Problems for Exam 1
NOTE: These problems do not cover EVERYTHING. You should be able
to do these in 50 minutes.
Part A - Calculator Allowed
1. Given the matrix A and vector b below, using only rational numbers,
nd the following: (a) RREF of [A|b]
MATH261 MAKEUP EXAM I SPRING 2013
NAME:
SI:
Problem Points
1
16
14
20
5
16
6
GOOD LUCK !
14
4
You may NOT use calculators or
any references. Show work to receive full credit. Circle the answer
for each problem.
2
3
SECTION NUMBER:
20
Total
100
Score
1. Ma
Department of Mathematics
Fall 2013, MATH 369
Colorado State University
Homework Assignment VI
Due Dec 2, 2013
1. Let the matrix A be given by
4
A = 2
2
0
1
0
1
0 ,
1
(a) Find the eigenvalue, eigenvectors of the matrix;
(b) Is A diagonalizable?
(b) Find t
Department of Mathematics
Fall 2013, MATH 369
Colorado State University
Homework Assignment V
Due Nov 1, 2013
1. Let P2 be the space of polynomials of degree less than 2. Prove that
p1 = 1 + 2x + x2 ,
p2 = 2 + 9x,
p3 = 3 + 3x + 4x2
is a basis of P2 . Then
Department of Mathematics
Fall 2013, MATH 369
Colorado State University
Homework Assignment IV
Due Oct 18, 2013
1. (A variation of Problem 5 in HW3) There are three points u = (3, 1, 2), v = (4, 0, 8) and w = (6, 1, 4).
Let l be the line passing through u
Department of Mathematics
Fall 2013, MATH 369
Colorado State University
Homework Assignment III
Due Oct 7, 2013
1. Let the matrix A be given by
55
1 0 .
43
2
A = 1
2
(a) Find adj(A).
(b) Use adj(A) to nd A1 .
(c) Use Cramers rule to solve Ax = b where b =
Department of Mathematics
Fall 2013, MATH 369
Colorado State University
Homework Assignment II
Due Sep 23, 2013
1. Let the matrix A be
A=
2
12
14
2
1 3
1
11 17 12
3 27 3
26
18 28
.
(a) Write the elementary matrices P1 , P2 , , Pn such that Pn Pn1 P2 P1 A
Name:
CSI:
Final Exam , Math 369
May 10, 2012
Part A
1. For A given below complete the following
(a)
(b)
(c)
(d)
Find a basis for the null space of A.
Find a basis for the row space of A.
Check that the null space and row spaces of A are orthogonal.
Find