MT210 MIDTERM 1 SAMPLE 1
ILKER S. YUCE
FEBRUARY 16, 2011
QUESTION 1. SYSTEMS OF LINEAR EQUATIONS
Determine the values of k such that the linear system
9x1
kx1
+ kx2
+
x2
is consistent.
1
=
9
= 3
QUESTION 2. ROW REDUCTION AND ECHELON FORMS
Determine when t
MT210 QUIZ 2
LKER S. YCE
FEBRUARY 8, 2011
Surname, Name:
QUESTION 1. 1.3 VECTOR EQUATIONS
Determine if b is a linear combination of a1 , a2 and a3 . If it is, nd the
weights c1 , c2 , c3 so that c1 a1 + c2 a2 + c3 a3 = b.
2
1
0
5
b = 1 , a1 = 2 , a2 = 1 ,
MT210 QUIZ 2
LKER S. YCE
FEBRUARY 4, 2011
Surname, Name:
QUESTION 1. 1.3 VECTOR EQUATIONS
Determine if b is a linear combination of a1 , a2 and a3 . If it is, nd the weights
c1 , c2 , c3 so that c1 a1 + c2 a2 + c3 a3 = b.
2
1
0
5
b = 1 , a1 = 2 , a2 = 1 ,
Linear Algebra Notes
Chapter 2
SOLUTIONS TO EXERCISES
Exercise 2.1. Show that scalar matrices commute with all other matrices.
Solution:
a
0
0
a
xy
ax ay
=
,
zw
az aw
while
xy
zw
a
0
0
xa ya
=
.
a
za wa
These are the same.
Exercise 2.2. Suppose a = d. Sho
Spring 2016: Math 2210
Problem Set 5
Due: March 4
Problem 1 Let W be the union of the first
andthird quadrants of the xy-plane
(including
x
the coordinate axes). Said differently, W =
R2 such that xy 0 . Is W a
y
subspace of R2 ? Explain.
Ans:
No,
W
i
Easier practice
Honors Linear Algebra (Math 230) Spring 2011
Practice Final Exam
There are twelve problems in this exam.
Points (given in parenthesis) add to 105. You will be graded for 100.
Show all work.
Provide appropriate justifications where requ
Very good practice, couple
interesting variations on standard
problems
Practice Problems for Final Exam
Math 217, Linear Algebra
2
3
1 2 3 0
62 0
1 07
7
(1) Let A = 6
4 3 2 2 05.
1 2 4 0
(a) Compute the reduced row echelon form of A.
(b) Find a basis for
Excellent practice. Solutions in another pdf
Linear Algebra (MATH 3333 04) Spring 2011
Final Exam Practice Problems
Instructions: Try the following on your own, then use the book and notes where you need help. Afterwards,
check your solutions with mine on
Answers available. Not a great exam, but #4 is worth looking at
MATH240: Linear Algebra
Final exam solutions
7/24/2015 Page 1
Write legibly and show all work. No partial credit can be given for an unjustified, incorrect
answer. Put your name in the top ri
This exam looks hard, especially the true/false
But we did learn the tools to answer these!
Math 33 AH : Practice Final Exam
Honors Linear Algebra and Applications
Instructor: Ciprian Manolescu
You have 3 hours. No books, notes or calculators are allowed.
Excellent practice. First 9 questions are repetitive.
#21 and 22 are nice questions
Prof. A. Suciu
MTH U371LINEAR ALGEBRA
PRACTICE FINAL EXAM
Spring 2005
1. Are the following vectors independent or dependent? If they are independent, say why. If they are
Linear Algebra (MATH 3333 04) Spring 2011
Final Exam Practice Problem Solutions
Instructions: Try the following on your own, then use the book and notes where you need help. Afterwards,
check your solutions with mine online. For Sections 1 and 2, no expla
MATH240: Linear Algebra
Final exam solutions
7/24/2015 Page 1
Write legibly and show all work. No partial credit can be given for an unjustified, incorrect
answer. Put your name in the top right corner and sign the honor pledge at the end of the
exam. If
Practice Test 2
1. Suppose that A is 6 10 matrix of rank 4. Determine each of the following numbers:
(a) dim(N ull(A)=
(b) dim(Row(A)=
(c) dim(Col(AT )=
2. Let a linear map T : R2 R2 map a triangle with vertices (0, 0), (1, 0), (0, 1) to the
triangle with
Practice Test 1
1. Solve the following system of equations:
x2 + 4x3 = 5
x1 + 3x2 + 5x3 = 2
3x1 + 7x2 + 8x3 =
6
2. Let the following matrix represent an augmented matrix of a linear system with 4 variables:
1 2 3 4 5
0 6 7 8 9
0 0 2 4 6
0 0 0 h s
Answer t
Math 210 Linear Algebra
Exam II Solutions
0
1. (10) Find the kernel of the matrix A = 6
3
4
2
4
2
7 .
5
Solution: R(2, 1, 2).
3
2. (15) Find an eigenvector for the matrix A = 3
4
1
1
1
0
1 .
1
Solution: PA (x) = (x 1)3 , evec: (1,-2,3). Up to scalar, this
Math 210 Linear Algebra
Exam I solutions
October 11, 2011
This exam has three pages with six questions in all, with point totals as shown, for a total of 100 points.
Calculators, cell-phones and other Partial credit will be given for partial progress towa
MT210 QUIZ 3
LKER S. YCE
FEBRUARY 11, 2011
Surname, Name:
QUESTION 1. 1.5 SOLUTION SETS OF LINEAR SYSTEMS
A) Find the general solution of the homogeneous system:
x1
x1
2x1
+
x2
+ 2 x2
+ 3 x2
+ x3
x3
=0
=0
=0
1
B) Verify that p = 1 is a particular solutio
MT210 QUIZ 4
LKER S. YCE
FEBRUARY 25, 2011
Surname, Name:
QUESTION 1. 1.5 SOLUTION SETS OF LINEAR SYSTEMS
A) Find the solution set of the linear system in the parametric-vector form:
4x1
2x1
6x1
+ 2 x2
+
x2
+ 3 x2
+ 6 x3
+ 3 x3
+ 9 x3
=
=
=
2
1
3
B) Find
MT210 QUIZ 4
LKER S. YCE
MARCH 21, 2010
Surname, Name:
QUESTION 1. 1.5 SOLUTION SETS OF LINEAR SYSTEMS
A) Find the solution set of the linear system in the parametric-vector form:
4x1
2x1
6x1
+ 2 x2
+
x2
+ 3 x2
+ 6 x3
+ 3 x3
+ 9 x3
=
=
=
2
1
3
B) Find the
MT210 QUIZ 1
LKER S. YCE
FEBRUARY 1, 2011
Surname, Name:
QUESTION 1. 1.1 LINEAR EQUATIONS IN LINEAR ALGEBRA
Please mark the following statement as TRUE or FALSE:
Every elementary row operation is reversible.
ANSWER 1.
TRUE.
QUESTION 2. 1.1 LINEAR EQUATION
MT210 QUIZ 1
LKER S. YCE
JANUARY 29, 2010
Surname, Name:
QUESTION 1. 1.1 LINEAR EQUATIONS IN LINEAR ALGEBRA
Please mark the following statement as TRUE or FALSE:
Every elementary row operation is reversible.
QUESTION 2. 1.1 LINEAR EQUATIONS IN LINEAR ALGE
MT210 TEST 2 SAMPLE 1
ILKER S. YUCE
MARCH 29, 2011
QUESTION 1. THE MATRIX OF A LINEAR TRANSFORMATION
Dene the linear transformation T : R2
R3 so that
]
[
x1 x2
x1
x1 + 2x2 .
x2
x1 + x2
a.) Find the standard matrix of T .
b.) Is T one-to-one?
c.) Is T ont
MT210 MIDTERM 1 SAMPLE 1
ILKER S. YUCE
FEBRUARY 16, 2011
QUESTION 1. SYSTEMS OF LINEAR EQUATIONS
Determine the values of k such that the linear system
9x1
kx1
+ kx2
+
x2
=
9
= 3
is consistent.
ANSWER
We apply row-reduction algorithm to the augmented matri
MT210 TEST 2 SAMPLE 1
ILKER S. YUCE
APRIL 3, 2011
QUESTION 1. THE MATRIX OF A LINEAR TRANSFORMATION
Dene the linear transformation T : R2
R3 so that
]
[
x1 x2
x1
x1 + 2x2 .
x2
x1 + x2
a.) Find the standard matrix of T . b.) Is T one-to-one? c.) Is T onto
MT210 TEST 3 SAMPLE 1
ILKER S. YUCE
APRIL 19, 2011
QUESTION 1. THE PROPERTIES OF DETERMINANTS
Find the determinant of the matrix below. Specify whether the matrix has an inverse without trying to
compute the inverse.
2 2 2 2
2
2
3
0
2 2
2
0
1 1 3 1
ANSW
MT210 TEST 3 SAMPLE 1
ILKER S. YUCE
APRIL 19, 2011
QUESTION 1. THE PROPERTIES OF DETERMINANTS
Find the determinant of the matrix below. Specify whether the matrix has an inverse without trying to
compute the inverse.
2 2 2 2
2
2
3
0
2 2
2
0
1 1 3 1
1
QU