Gaussian Elimination to Solve a 3 by 3 System of Equations
9K views · Oct 4, 2022 analyzemath.com
This video has three objectives: 2 - Explains what is an augmented matrix 2 - Explains what is a matrix in row echelon form 2 - Use the Gaussian Elimination method to rewrite the augmented matrix in row echelon form 3 - Use back substitution to solve the system. The augmented matrix is written from the given system and then rewritten in row echelon form. We then rewrite the system and solve it by back substitution. More at https://www.analyzemath.com/linear-algebra.html More at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Inverse of a 3 by 3 Matrix Using Gauss-Jordan Method
11K views · Oct 4, 2022 analyzemath.com
This video goes through the steps in finding the inverse of a 3 by 3 matrix. There are three objectives 1 - Explain what is a matrix in reduced row echelon form (rref) 2- Write the augmented matrix of the equation to solve 3 - Use the basic row elementary operations to rewrite the augmented matrix in reduced row echelon form 4 - Read the inverse matrix All the detailed steps are explained in the videos starting from the augmented matrix to reading the final answer which is the inverse matrix. More at https://www.analyzemath.com/linear-algebra.html More at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Solve 2 by 2 System of Equations by Elimination
204K views · Oct 3, 2022 analyzemath.com
This video shows how to solve systems of equations using the method of elimination. The two basic operations that may be used to rewrite the system of equations into an equivalent one (i.e.with the same solutions) are 1 - multiply equations by a constant and 2 - add/subtract equations. These operations are well explained and applied. Four examples are presented including a simple example to explain the idea of elimination, an example with completely different coefficients, an example with no solutions, and an example with an infinite number of solutions. Graphical interpretations of solutions are also included where the equations in the system of equations are graphed: A system with one solution corresponds to two lines intersecting at one point, a system with no solution corresponds to two parallel lines and hence no point of intersection and finally, a system with an infinite number of solutions where the given equations are equivalent and therefore represent one equation in two variables. More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More grade 11 math practice at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html
Eigenvalues and Eigenvectors of a 2 by 2 Matrix
41K views · Oct 3, 2022 analyzemath.com
The video starts with the necessary definitions of parallel vectors and the eigenvalues and eigenvectors using numerical examples. Then the calculations start with the main equation of eigenvectors: AX = Lambda X. The condition of the determinant of the matrix A - Lambda I being equal to zero leads to the characteristic equation which when solved gives solutions called the eigenvalues. With the knowledge of the eigenvalues, the eigenvectors are then calculated. We go even further and check that one eigenvector and its corresponding eigenvalue satisfies the equation: AX - Lambda X. This video gives a truly deep analysis of the concept and the calculation skills of eigenvectors and eigenvalues. More at https://www.analyzemath.com/linear-algebra.html More at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Eigenvalues and Eigenvectors of a 3 by 3 Matrix
2K views · Oct 3, 2022 analyzemath.com
This video is about calculating the eigenvalues and eigenvectors of a 3 by 3 matrix. It includes 5 learning objectives: 1 - Review of Eigenvalues and Eigenvectors - 2 - Review the equation A V = Lambda V, which defines the Eigenvalues and Eigenvectors and the conditions - 3 - Write and solve the characteristic equation - 4 - Calculate the Eigenvectors - 5 - Check both the Eigenvalues and Eigenvectors against the equation. The author explains the concept, calculates the Eigenvalues and Eigenvectors with all the details, and checks both the Eigenvalues and Eigenvectors against the equation A V = Lambda V. More on Eigenvalues and Eigenvectors at http://www.analyzemath.com/linear-algebra/matrices/eigenvalues-and-eigenvectors-questions-with-solutions.html More at https://www.analyzemath.com/linear-algebra.html More at https://www.analyzemath.com/high_school_math/grade_11/grade-11-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com More grade 12 math practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html Subscribe to my channel to get more videos on math for all levels https://www.youtube.com/channel/UC2cmvDflm86w7C_D7QmcOVA? sub_confirmation=1
Use Dot Product to Find the Angle between Two vectors
19K views · Feb 20, 2022 analyzemath.com
The dot product is used to find the angle between two 3D vectors. more at: www.analyzemath.com/high_school_math/grade_12/scal_cross.html
Calculate the Determinant of a 3 by 3 Matrix
8K views · Dec 30, 2022 analyzemath.com
This video presents the steps needed to find the determinant of a 3 by 3 matrix using determinants of 2 by 2 matrices.