Linear Algebra
Linear Algebra
Required or Elective:
Course Prerequisites: Math 31132
Catalog Description:
System of Linear Equations: row-echelon form, reduced row-echelon form, Gaussian elimination, Gauss-Jordan method, etc. Matrices: arithmetic's, operations, multiplications, properties of matrix arithmetic's matrix transpose, inverse, special matrices, etc. Determinants: the determinant function, properties of determinants, the method of co-factors, ad joint matrix, using row reduction to compute determinants, Cramer's rule. Euclidean n-space: introduction, vectors, dot product, cross product, Euclidean n-space, linear transformations. Vector spaces: vector spaces, sub-spaces, span, linear independence/dependence, basis and dimensions, change of basis, fundamental sub-spaces, inner product spaces, orthonormal basis, least squares, QR-decomposition, orthogonal matrices. Eigenvalues and Egienvectors: review of determinants, Eigenvalues and Egienvectors, diagonalization.
Textbook and Related Course Materials:
Text Book: Advanced Engineering Mathematics, seventh edition or above. Erwin Kreyszig, John Wiley and Sons, Inc.
Topics Covered:
System of linear equations 5 hrs
Matrices 8 hrs
Determinants 5 hrs
Euclidean n-space 6 hrs
Vector spaces 15 hrs
Eigenvalues, Eginevectors 5 hrs
Contribution to the Professional Component:
Engineering Topics: 0 %
General Education: 0 %
Mathematics & Basic Sciences: 100 %
Expected Level of Proficiency for Students Entering the Course: Mathematics (Some).
Will This Course Involve Computer Assignments? No.
Will This Course Have TA(s) When it is Offered? No.
CLO's: Upon completion of this course, students will have had an opportunity to attain knowledge of:
Solve a system of linear equations using Gauss-Jordan Elimination, Gaussian Elimination, Cramer’s Rule, and the inverse wherever it is.
Perform matrix addition, scalar multiplication and matrix multiplication.
Evaluate determinant by row reduction or or cofactor expansion.
Use vector space properties to decide whether a given subset is a subspace or not.
Find a basis of a vector, row, column and null spaces.
Identify the inner product spaces.
Construct an orthonormal basis by applying the Gram-Schmidt process.
Demonstrate proficiency in finding eigenvalues and eigenvectors of a matrix, and in determining if a matrix is diagonalizable.
Define the linear transformations and find bases for the kernel and range.
ABET – Student Outcomes (1-7)
1. an ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.
2. an ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors.
3. an ability to communicate effectively with a range of audiences.
4. an ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts.
5. an ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives.
6. an ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.
7. an ability to acquire and apply new knowledge as needed, using appropriate learning strategies.
Chapter 5: Eigenvalues and eigenvectors
Revision class pdf
Required or Elective:
Course Prerequisites: Math 31132
Catalog Description:
System of Linear Equations: row-echelon form, reduced row-echelon form, Gaussian elimination, Gauss-Jordan method, etc. Matrices: arithmetic's, operations, multiplications, properties of matrix arithmetic's matrix transpose, inverse, special matrices, etc. Determinants: the determinant function, properties of determinants, the method of co-factors, ad joint matrix, using row reduction to compute determinants, Cramer's rule. Euclidean n-space: introduction, vectors, dot product, cross product, Euclidean n-space, linear transformations. Vector spaces: vector spaces, sub-spaces, span, linear independence/dependence, basis and dimensions, change of basis, fundamental sub-spaces, inner product spaces, orthonormal basis, least squares, QR-decomposition, orthogonal matrices. Eigenvalues and Egienvectors: review of determinants, Eigenvalues and Egienvectors, diagonalization.
Textbook and Related Course Materials:
Text Book: Advanced Engineering Mathematics, seventh edition or above. Erwin Kreyszig, John Wiley and Sons, Inc.
Topics Covered:
System of linear equations 5 hrs
Matrices 8 hrs
Determinants 5 hrs
Euclidean n-space 6 hrs
Vector spaces 15 hrs
Eigenvalues, Eginevectors 5 hrs
Contribution to the Professional Component:
Engineering Topics: 0 %
General Education: 0 %
Mathematics & Basic Sciences: 100 %
Expected Level of Proficiency for Students Entering the Course: Mathematics (Some).
Will This Course Involve Computer Assignments? No.
Will This Course Have TA(s) When it is Offered? No.
CLO's: Upon completion of this course, students will have had an opportunity to attain knowledge of:
Solve a system of linear equations using Gauss-Jordan Elimination, Gaussian Elimination, Cramer’s Rule, and the inverse wherever it is.
Perform matrix addition, scalar multiplication and matrix multiplication.
Evaluate determinant by row reduction or or cofactor expansion.
Use vector space properties to decide whether a given subset is a subspace or not.
Find a basis of a vector, row, column and null spaces.
Identify the inner product spaces.
Construct an orthonormal basis by applying the Gram-Schmidt process.
Demonstrate proficiency in finding eigenvalues and eigenvectors of a matrix, and in determining if a matrix is diagonalizable.
Define the linear transformations and find bases for the kernel and range.
ABET – Student Outcomes (1-7)
1. an ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics.
2. an ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors.
3. an ability to communicate effectively with a range of audiences.
4. an ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts.
5. an ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives.
6. an ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions.
7. an ability to acquire and apply new knowledge as needed, using appropriate learning strategies.
Below are some problem solving videos