MAE 3323 Mechanical Design 1
Course Project
PROBLEM STATEMENT:
Consider the tower shown in the figure. Due to its good weld ability, we plan to use ASME SA
285 Grade C material for fabricating the pre
MATH 4063-5023
Homework Set 5
1. Find the
20
(a) 0 2
00
characteristic polynomials and minimal polynomials of the following matrices.
0
0
2
The characteristic polynomial of this matrix is
2
0
0
2
0 =
MATH 4063-5023
Solutions to Homework Set 6
1. Determine if the following matrices A are diagonalizable. When A is diagonalizable, provide both the
matrix C diagonalizing A and its diagonal form D (so
MATH 4063-5023
Solutions to Homework Set 2
1. Use elementary row operations to systematically transform the following matrices to row echelon form.
1 2 1 0
(a) 2 3 0 1
1 2 1 1
We have
1
2
1
2
3
2
1
MATH 4063-5023
Solutions to Homework Set 4
1. Let P be the vector space of polynomials with indeterminant x.Which of the following mappings are
linear transformations from P to itself
(a) T : p xp
Le
MATH 4063-5023
Solutions to Homework Set 3
1. Let F be a eld with exactly two elements (it will be isomorphic to Z2 ) and let V be a 2-dimensional
vector space over F. How many vectors are there in V
MATH 4063-5023
Homework Set 3
1. Let F be a eld with exactly two elements (it will be isomorphic to Z2 ) and let V be a 2-dimensional
vector space over F. How many vectors are there in V ? How many di
MATH 4063-5023
Homework Set 4
1. Let P be the vector space of polynomials with indeterminant x.Which of the following mappings are
linear transformations from P to itself
(a) T : p xp
(b) T : p 2p
(c)
MATH 4063-5023
Homework Set 6
1. Determine if the following matrices A are diagonalizable. When A is diagonalizable, provide both the
matrix C diagonalizing A and its diagonal form D (so that D = C1 A
MATH 4063-5023
Homework Set 5
1. Find the
2 0
(a) 0 2
0 0
2
(b) 0
0
characteristic polynomials and minimal polynomials of the following matrices.
0
0
2
1
1
2
1
2
0
2. Find the eigenvalues of the fol
MATH 4063-5023
Solutions to Homework Set 2
1. Use elementary row operations to systematically transform the following matrices to row echelon form.
0
1
1210
1A
(a) @ 2 3 0
121
1
We have
0
1
@2
1
2
3
2
Math 4063-5023
SOLUTIONS TO FIRST EXAM
2:30 3:20 , October 23, 2013
1. Denitions. Write down the precise denitions of the following notions. (3 pts each)
(a) dependence relation.
A dependence relatio
MATH 4063-5023
Solutions to Homework Set 1
1. Let F be a eld, and let Fn denote the set of n-tuples of elements of F, with operations of scalar
multiplication and vector addition dened by
for all F an
MATH 4063-5023
Homework Set 1
1. Let F be a eld, and let Fn denote the set of n-tuples of elements of F, with operations of scalar
multiplication and vector addition dened by
[
[
1; : : : ;
n]
1; : :