1.1 and1.2
Chapter 1
Matrices and Systems of Linear Equations
1.1: Introduction to Matrices and Systems of Linear Equations
1.2: Echelon Form and Gauss-Jordan Elimination
Lecture Linear Algebra - Math 2568M on Friday, January 11, 2013
MW 605
Oguz Kurt
Math 2568, Section 110 Quiz 1
Name:
Show all your work, and indicate clearly if you continue on the back. Each of the two problems is worth 5 points.
1. Find all values of a for which the following system has no solution.
x1 + 2x2 = 3
ax1 2x2 = 5
Applying
Math 2568, Section 90 Quiz 3
Name:
Show all your work, and indicate clearly if you continue on the back. Each of the two problems is worth 5 points.
a
0
1. For what value(s) of the scalar a R are the vectors v1 =
and v2 =
linearly independent?
7
0
By de
Math 2568, Section 35 Quiz 3
Name:
Show all your work, and indicate clearly if you continue on the back. Each of the two problems is worth
1
1. Determine which choice(s) of the scalar a R make(s) it so that the vectors v1 = 2 , v2 =
3
a
v3 = 8 are line
Math 2568, Section 110 Quiz 3
Name:
Show all your work, and indicate clearly if you continue on the back. Each of the two problems is worth 5 points.
2 7
5 0
1. Define the matrices A =
and B =
. Compute the matrices A1 and B 1 (you may write
4 9
0 2
each
Math 2568, Section 110 Quiz 2
Name:
Show all your work, and indicate clearly if you continue on the back. Each of the two problems is worth 5 points.
1. Does the linear system corresponding to the augmented matrix
1 37 0 8.44321 5 0 5
0 0 1
0
5 0 2
0 0 0
Math 2568, Section 90 Quiz 4
Name:
Show all your work, and indicate clearly if you continue on the back. Each of the two problems is worth 5 points.
1. Find a nonzero vector v that is perpendicular to the plane containing the three points (1, 1, 1), (2, 3
Math 2568, Section 35 Quiz 4
Name:
Show all your work, and indicate clearly if you continue on the back. Each of the two problems is worth 5 points.
~ that B = (0, 0), that w points in the same direction as the vector 3 , and that
1. Suppose that w = AB,
Math 2568, Section 110 Quiz 4
Name:
Show all your work, and indicate clearly if you continue on the back. Each of the two problems is worth 5 points.
7
0
1. Find the area of the parallelogram whose edges are the vectors u = 2 and v = 1 .
3
2
The area is
i
Math 2568, Section 90 Quiz 1
Name:
Show all your work, and indicate clearly if you continue on the back. Each of the two problems is worth 5 points.
1. Given the values a11 = 2, a12 = 3, a21 = 4, a22 = 8, b1 = 11, b2 = 76, display the system of equations
Math 2568, Section 90 Quiz 2
Name:
Show all your work, and indicate clearly if you continue on the back. Each of the two problems is worth 5 points.
1 1
1. Let A =
. Explicitly describe all solutions x R2 to the equation xT Ax = 0.
1 1
Let us write x =
x1
Math 2568, Section 35 Quiz 2
Name:
Show all your work, and indicate clearly if you continue on the back. Each of the two problems is worth 5 points.
1. List all possibilities for the size of the solution set for a nonhomogenous system with one equation an
1.1 and1.2
Chapter 1
Matrices and Systems of Linear Equations
1.1: Introduction to Matrices and Systems of Linear Equations
1.2: Echelon Form and Gauss-Jordan Elimination
Lecture Linear Algebra - Math 2568M on Friday, January 11, 2013
MW 605
Oguz Kurt
1.3 Consistent
Systems of Linear
Equations
Chapter 1
1.5 Matrix
Matrices and Systems of Linear Equations
1.6: Algebra of
Operations
Matrix Operations
1.3 Consistent Systems of Linear Equations
1.5 Matrix Operations
Lecture Linear Algebra - Math 2568M
Practice Midterm 1
Math 2568
Autumn 2013
Oguz Kurt
Problem 1
Suppose A is an n m matrix and B is an m n matrix. Then (AB )T = AT B T .
Solution
.
False
Problem 2
Suppose A and B are n n matrices. Then (A + B ) (A + B ) = A2 + 2 AB + B 2 .
Solution
.
False
Quiz 4
Autumn 2013
Name:
Math 2568
There are two problems on this quiz; make sure to look at the back.
Problem 1 (6 points)
41
. For six points, determine whether A is singular or nonsingular. For full credit, be sure to show
51
your work and to explain y
Quiz 3
Name:
Autumn 2013
Math 2568
There are two problems on this quiz; make sure to look at the back.
Problem 1 (6 points)
3
Let A = 1
2
3
1 and B =
1
2
2
1
2
. For six points, compute AB .
Solution
.
Problem 2 (6 points)
1
Let A = 1
2
1 2
2
2
1 and v =
Quiz 2
Math 2568
Autumn 2013
Oguz Kurt
There are two problems on this quiz; make sure to look at the back.
Problem 1 (6 points)
The matrix
0
0
0
101
2 1 2
1 1 3
is the augmented matrix for a system of linear equations. Give the vector form for the genera
Quiz 1
Name:
Autumn 2013
Math 2568
There are two problems on this quiz; make sure to look at the back.
Problem 1 (6 points)
Write down the augmented matrix corresponding to the following system of linear equations.
x1 + 4 x2
8 x3 + 4 x4 = 6
2 x1 + 5 x2 +
Practice for Quiz 3
Name:
Autumn 2013
Math 2568
This is version 74130 of the practice quiz.
Problem 1
2
Let A = 2
2
2 3
2
1
2 and B = 2
3 3
1
3
3
3
2
1 . Compute AB and BA.
2
Solution
.
Problem 2
Let A =
3
2
3
2
and B =
3
2
1
3
. Compute A + (4) B .
Solut
Quiz 5
Name:
Autumn 2013
Math 2568
Problem 1 (6 points)
Let v = (0, 2, 4) and w = (1, 3, 3) and x = (0, 0, 2) . For six points, compute x (v w).
Solution
.
Problem 2 (6 points)
Find a vector perpendicular to both (2, 3, 5) and (3, 1, 5) .
Solution
.
Probl
Quiz 4
Autumn 2013
Name:
Math 2568
Problem 1 (6 points)
222
Let A = 3 5 4 . For six points, determine whether A is singular or nonsingular. For full credit, be sure to
325
show your work and to explain your reasoning.
Solution
.
Problem 2 (6 points)
For s
2.1 Vectors in the
Plane
Chapter 2
Vectors in 2-Space and 3-Space
2.1 Vectors in the Plane
Lecture Linear Algebra - Math 2568M on February 6, 2013
MW 605
Oguz Kurt
oguz@math.ohio-state.edu
292-9659
Off. Hrs:
MWF 10:20-11:20
The Ohio State University
2.1
2
1.7 Linear
Independence and
Nonsingular Matrices
Chapter 1
Matrices and Systems of Linear Equations
1.7 Linear Independence and Nonsingular Matrices
Lecture Linear Algebra - Math 2568M on January 25, 2013
MW 605
Oguz Kurt
oguz@math.ohio-state.edu
292-965
1.3 Consistent
Systems of Linear
Equations
1.5 Matrix
Chapter 1
Operations
Matrices and Systems of Linear Equations
1.3 Consistent Systems of Linear Equations
1.5 Matrix Operations
Lecture Linear Algebra - Math 2568M on January 14, 2013
MW 605
Oguz Ku
1.3 Consistent
Systems of Linear
Equations
1.5 Matrix
Chapter 1
Operations
Matrices and Systems of Linear Equations
1.3 Consistent Systems of Linear Equations
1.5 Matrix Operations
Lecture Linear Algebra - Math 2568M on January 14, 2013
MW 605
Oguz Ku
Math 2568, Section 35 Quiz 1
Name:
Show all your work, and indicate clearly if you continue on the back. Each of the two problems is worth 5 points.
1. Give the augmented matrix corresponding to the following system of linear equations.
7x1 + 4x2 + 3x3 7x