STUDY GUIDE FOR MAS 2103 MID-TERM EXAM
Be able to do each of the following:
1. Solve a system of equations by Gauss elimination and back-substitution.
2. Solve a system of equation by Gauss-Jordan elimination.
3. Use Gauss-Jordan elimination to find A-1,
MAC 2103
Module 12
Eigenvalues and Eigenvectors
1
Learning Objectives
Upon completing this module, you should be able to:
1.
2.
3.
4.
5.
6.
Solve the eigenvalue problem by finding the eigenvalues
and the corresponding eigenvectors of an n x n matrix.
Find
MAC 2103
Module 11
lnner Product Spaces II
1
Learning Objectives
Upon completing this module, you should be able to:
1.
2.
3.
4.
5.
6.
Rev.F09
Construct an orthonormal set of vectors from an
orthogonal set of vectors.
Find the coordinate vector with respe
MAC 2103
Module 10
lnner Product Spaces I
1
Learning Objectives
Upon completing this module, you should be able to:
1.
Define and find the inner product, norm and distance in a
given inner product space.
2.
Find the cosine of the angle between two vectors
MAC 2103
Module 9
General Vector Spaces II
1
Learning Objectives
Upon completing this module, you should be able to:
1.
Find the coordinate vector with respect to the standard basis for
any vector in .
2.
Find the coordinate vector with respect to another
MAC 2103
Module 8
General Vector Spaces I
1
Learning Objectives
Upon completing this module, you should be able to:
1. Recognize from the standard examples of vector
spaces, that a vector space is closed under vector
addition and scalar multiplication.
2.
MAC 2103
Module 7
Euclidean Vector Spaces II
1
Learning Objectives
Upon completing this module, you should be able to:
1.
2.
3.
4.
Rev.F09
Determine if a linear operator in n is one-to-one.
Find the inverse of a linear operator in n .
Use the images of th
MAC 2103
Module 6
Euclidean Vector Spaces I
1
Learning Objectives
Upon completing this module, you should be able to:
1. Use vector notation in n.
2. Find the inner product of two vectors in n.
3. Find the norm of a vector and the distance between
two vec
MAC 2103
Module 5
Vectors in 2-Space and 3-Space II
1
Learning Objectives
Upon completing this module, you should be able to:
1. Determine the cross product of a vector in 3.
2. Determine a scalar triple product of three vectors in
3.
3. Find the area of
MAC 2103
Module 4
Vectors in 2-Space and 3-Space I
1
Learning Objectives
In this module, we apply our earlier ideas specifically to vectors
in 2-space, 2, (in the xy-plane) in two dimensions and to
vectors in 3-space, 3,(in the xyz-space) in three
dimensi
MAC 2103
Module 3
Determinants
1
Learning Objectives
Upon completing this module, you should be able to:
1.
Determine the minor, cofactor, and adjoint of a matrix.
2.
Evaluate the determinant of a matrix by cofactor
expansion.
3.
Determine the inverse of
MAC 2103
Module 2
Systems of Linear Equations and
Matrices II
1
Learning Objectives
Upon completing this module, you should be able to :
1.
2.
3.
4.
5.
Find the inverse of a square matrix.
Determine whether a matrix is invertible.
Construct and identify e
MAC 2103
Module 1
Systems of Linear Equations and
Matrices I
1
Learning Objectives
Upon completing this module, you should be able to:
1.
Represent a system of linear equations as an augmented
matrix.
2.
Identify whether the matrix is in row-echelon form,
STUDY GUIDE FOR MAS 2103 FINAL EXAM
Be able to do each of the following:
1. Find the inner product, norm and distance.
!
2. Find the solution of the homogeneous system Ax = 0; use Gauss elimination on
!
!
[ A | 0 ] to obtain a row echelon form [G | 0 ] an