LINEAR ALGEBRA II (MAT 214)

About Course

Are you having issues in linear algebra? Then this course will help you get all the fundamentals and you are ending the course smiling.

I will not bore you

I take my courses very seriously but at the same time i try to make it fun since i know how difficult it is for students to learn mathematics. This course is fun, and when you need some energy to keep going, you will get it from me.

My Approach

Practice, practice and more practice. Every section in this course has a practice test and possible examination questions at the end.

Course Content

SYSTEMS OF LINEAR EQUATION
At the end of this section, you will learn: i. Basic definition, solution of linear equation. ii. Equivalent systems, elementary operations. iii. Small square systems of linear equations. iv. systems in triangular forms. v. Gaussian elimination.

LINEAR EQUATIONS AND SOLUTIONS

04:15
SYSTEM OF LINEAR EQUATIONS

04:33
EQUIVALENT SYSTEM, ELEMENTARY OPERATIONS

04:26
LINEAR EQUATION IN ONE UNKNOWN

03:21
SYSTEM OF TWO LINEAR EQUATIONS IN TWO UNKNOWN

06:26
SYSTEMS IN TRIANGULAR FORM

03:28
GAUSSIAN ELIMINATION

04:54
PRACTICE TEST

CANONICAL FORMS
At the end of this section, you will learn: 2.1 Rank of matrix 2.2 Normal forms(canonical form) 2.3 Rank of matrix by triangular form 2.4 Solution of simultaneous equations 2.5 Gauss- Jordan method 2.6 Consistency of a linear equation 2.7 Homogeneous equation.

RANK OF MATRIX

08:11
NORMAL FORMS

06:42
RANK OF MATRIX BY TRIANGULAR FORM

10:53
SOLUTION OF SIMULTANEOUS EQUATION

08:49
GAUSS-JORDAN METHOD

13:29
CONSISTENCY OF A LINEAR EQUATION

22:18
HOMOGENEOUS EQUATION

01:00
HOMOGENEOUS EQUATION (PROBLEM 1)

02:30
HOMOGENEOUS EQUATION (PROBLEM 2)

02:59
HOMOGENEOUS EQUATION (PROBLEM 3)

04:32
PRACTISE TEST

EIGENVALUES AND EIGENVECTORS
At the end of this section you will be able to solve problems on: eigenvalues and eigenvectors and lots more

EIGENVALUES

04:33
FIRST IMPORTANT PROPERTY OF EIGENVALUE

04:34
SECOND IMPORTANT PROPERTY OF EIGENVALUES.

03:10
THIRD IMPORTANT PROPERTY OF EIGENVALUES

02:32
FOURTH IMPORTANT PROPERTY OF EIGENVALUES

03:52
EIGENVALUES (PROBLEM 5)

02:20
EIGENVALUES (PROBLEM 6)

02:24
EIGENVALUES (PROBLEM 7)

03:18
EIGENVALUES (PROBLEM 8)

02:50
CAYLEY- HAMILTON THEOREM

05:47
CAYLEY- HAMILTON THEOREM ( PROBLEM 1 )

06:02
CAYLEY- HAMILTON THEOREM ( PROBLEM 2 )

02:27
POWER OF MATRIX (by cayley hamilton theorem)

05:52
EIGENVECTORS

04:48
EIGENVECTORS ( PROBLEM 2 )

01:26
NON-SYMMETRIC MATRICES WITH NON-REPEATED EIGENVALUES

06:03
NON-SYMMETRIC MATRICES WITH REPEATED EIGEN VALUES

03:39
SYMMETRIC MATRICES WITH NON-REPEATED EIGENVALUES
SYMMETRIC MATRICES WITH REPEATED EIGENVALUES

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About Course

What Will You Learn?

Course Content

SYSTEMS OF LINEAR EQUATION At the end of this section, you will learn: i. Basic definition, solution of linear equation. ii. Equivalent systems, elementary operations. iii. Small square systems of linear equations. iv. systems in triangular forms. v. Gaussian elimination.

LINEAR EQUATIONS AND SOLUTIONS

SYSTEM OF LINEAR EQUATIONS

EQUIVALENT SYSTEM, ELEMENTARY OPERATIONS

LINEAR EQUATION IN ONE UNKNOWN

SYSTEM OF TWO LINEAR EQUATIONS IN TWO UNKNOWN

SYSTEMS IN TRIANGULAR FORM

GAUSSIAN ELIMINATION

PRACTICE TEST

CANONICAL FORMS At the end of this section, you will learn: 2.1 Rank of matrix 2.2 Normal forms(canonical form) 2.3 Rank of matrix by triangular form 2.4 Solution of simultaneous equations 2.5 Gauss- Jordan method 2.6 Consistency of a linear equation 2.7 Homogeneous equation.

RANK OF MATRIX

NORMAL FORMS

RANK OF MATRIX BY TRIANGULAR FORM

SOLUTION OF SIMULTANEOUS EQUATION

GAUSS-JORDAN METHOD

CONSISTENCY OF A LINEAR EQUATION

HOMOGENEOUS EQUATION

HOMOGENEOUS EQUATION (PROBLEM 1)

HOMOGENEOUS EQUATION (PROBLEM 2)

HOMOGENEOUS EQUATION (PROBLEM 3)

PRACTISE TEST

EIGENVALUES AND EIGENVECTORS At the end of this section you will be able to solve problems on: eigenvalues and eigenvectors and lots more

EIGENVALUES

FIRST IMPORTANT PROPERTY OF EIGENVALUE

SECOND IMPORTANT PROPERTY OF EIGENVALUES.

THIRD IMPORTANT PROPERTY OF EIGENVALUES

FOURTH IMPORTANT PROPERTY OF EIGENVALUES

EIGENVALUES (PROBLEM 5)

EIGENVALUES (PROBLEM 6)

EIGENVALUES (PROBLEM 7)

EIGENVALUES (PROBLEM 8)

CAYLEY- HAMILTON THEOREM

CAYLEY- HAMILTON THEOREM ( PROBLEM 1 )

CAYLEY- HAMILTON THEOREM ( PROBLEM 2 )

POWER OF MATRIX (by cayley hamilton theorem)

EIGENVECTORS

EIGENVECTORS ( PROBLEM 2 )

NON-SYMMETRIC MATRICES WITH NON-REPEATED EIGENVALUES

NON-SYMMETRIC MATRICES WITH REPEATED EIGEN VALUES

SYMMETRIC MATRICES WITH NON-REPEATED EIGENVALUES

SYMMETRIC MATRICES WITH REPEATED EIGENVALUES

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SYSTEMS OF LINEAR EQUATION
At the end of this section, you will learn: i. Basic definition, solution of linear equation. ii. Equivalent systems, elementary operations. iii. Small square systems of linear equations. iv. systems in triangular forms. v. Gaussian elimination.

CANONICAL FORMS
At the end of this section, you will learn: 2.1 Rank of matrix 2.2 Normal forms(canonical form) 2.3 Rank of matrix by triangular form 2.4 Solution of simultaneous equations 2.5 Gauss- Jordan method 2.6 Consistency of a linear equation 2.7 Homogeneous equation.

EIGENVALUES AND EIGENVECTORS
At the end of this section you will be able to solve problems on: eigenvalues and eigenvectors and lots more