MATH 1410
Solutions for Homework 5
Submitted Friday, March 1, 2013
(1) Row reduce the following matrices to [reduced row] echelon form. (Make sure you specify your
row operations.)
3
5
6
1
0
5
0
(a)
MATH 1410
Solutions for Homework 9
Submitted Friday, April 5, 2013
(1) Calculate the rank of
2 4
1
2
1 2
0
1
1
1
3 .
4
2
2
4
([The rank] of a matrix is the number of pivot elements in the echelon for
MATH 1410
Solutions for the Sample Midterm
(1) Find the roots of the following polynomials:
(a) (x 1) x2 + 5x + 6
Solution:
Let a and b be numbers. Then,
(x + a)(x + b) = x2 + ax + bx + ab = x2 + (a +
MATH 1410
Solutions for Homework 8
Submitted Thursday, March 28, 2013
For all of the questions below, let
A =
and let
1
0
0 2
0
3
0
4
5
0
1
0
= 0 , = 1 , = 0 .
e1
e2
e3
0
0
1
(1) Find [a] vector 1 s
Sample Final - Answers
(1) The RREF of the matrix corresponding to this system of equation is
1 0 0 35/11
0 1 0
3/11
0 0 1 29/11
which shows a = 35/11, b = 3/11, and c = 29/11.
(2) A REF of the matri
MATH 1410
Solutions for Homework 6
Submitted Friday, March 8, 2013
(1)
1
1
(a) Show that R2 = span
1
1
,
.
Solution:
The span of vectors , , . . . (all from Rn ) is the set of all their linear combi
MATH 1410
Solutions for Homework 1
Submitted Friday, January 18
(1) Solve the following systems of equations:
(a)
5x + y = 59
x + 5y = 31.
Solution:
There are many ways to solve this. Here are four:
M
MATH 1410
Solutions for Homework 4
Submitted Friday, February 15, 2013
(1) Row reduce the following matrices. (Make sure you specify your row operations.)
1
5
6
2
5
(a) 2 11 11
3 10 20
5
Solution:
Le
MATH 1410
Solutions for Homework 3
(The mistake in the fth line on page 10 has been corrected)
Submitted Friday, February 1, 2013
(1) Draw the following vectors in standard position (i.e. starting at
MATH 1410
Solutions for Homework 2
Submitted Friday, January 25
(1) Find all solutions to the following systems of equations:
2x + 3y + 4z = 1
4x 9y + 16z = 1
(a)
3x + 3y
z = 2.
Solution:
Substituti
Sample, ugly row reduction.
This is a sample of row reduction when numbers dont work out nicely.
Example 1. Row reduce the matrix
9
1
3
5
79 1
3
22
1 4
1
1
3
0
1
3
13
0
0
1
to reduce row echelon for