WORKSHEET 2 - solutions
Math 53, GSI: Toni Antunovi
c
c
Problem 1. Consider the set of m n matrices whose entry at the intersection
of the rst row and rst column is a. For what values of a is this set
Quiz 2
Math 54, Section 203
GSI: Toni Antunovi
c
c
February 16, 2011
Solutions of all problems must by accompanied by relevant explanations.
Problem 1. Find the determinant of the matrix
1 2 1 3
3
0
1
Quiz 3
Math 54, Section 203
GSI: Toni Antunovi
c
c
March 16, 2011
Solutions of all problems must by accompanied by relevant explanations.
Problem 1. Find all eigenvalues of the matrix
4
2 2
1 4
A= 2
Quiz 4
Math 54, Section 203
GSI: Toni Antunovi
c
c
May 9, 2011
Solutions of all problems must by accompanied by relevant explanations.
Problem 1. Find the general solution to the equation
y 4y + 3 = 0
Quiz 5
Math 54, Section 203
GSI: Toni Antunovi
c
c
April 29, 2011
Solutions of all problems must by accompanied by relevant explanations.
Problem 1. Find the solution to the following initial problem
Quiz 2
Math 54, Section 208
GSI: Toni Antunovi
c
c
February 16, 2011
Solutions of all problems must by accompanied by relevant explanations.
Problem 1. For each of the following two matrices determine
Quiz 3
Math 54, Section 208
GSI: Toni Antunovi
c
c
March 16, 2011
Solutions of all problems must by accompanied by relevant explanations.
Problem 1. Find all eigenvalues of the matrix
6 2
2
3
A = 6 1
Quiz 4
Math 54, Section 208
GSI: Toni Antunovi
c
c
April 13, 2011
Solutions of all problems must by accompanied by relevant explanations.
Problem 1. Find the solution to the dierential equation
y 6y +
Quiz 5
Math 54, Section 208
GSI: Toni Antunovi
c
c
April 29, 2011
Solutions of all problems must by accompanied by relevant explanations.
Problem 1. Find the largest interval on which you can conclude
Problem 1. If
A=
2
1
0
, B = 1
1
34
05
1
0 , C =
2
2
3
1
0
determine which of these expressions are well-dened and calculate those which
are.
a) A 2B
b) AB + 2C
c) A1 + BC T
d) C 1 + C T .
Solution:
a
Quiz 1
Math 54, Section 203
GSI: Toni Antunovi
c
c
Problem 1. Find all solutions to the system
3x1
x1
+ 2x 2
+
x2
x3
+ x3
+ x3
Solution:
+
x4
5 x4
2 x4
= 10
= 11
=4
001
1 10
Augmented matrix of this