Krista King Math
Solving Systems of Equations with Cramer's Rule
Show how matrices can be helpful for solving systems of equations. The video illustrates an example of solving a two-variable system utilizing Cramer's Rule. The instructor shows how to find the determinant of each matrix and then uses...
Khan Academy
Khan Academy: Linear Algebra: Deriving a Method for Determining Inverses
An instructional video that explains how the method for finding the inverse transformation matrix is derived. It is the same method for finding the inverse for any invertible matrix. [18:00]
Khan Academy
Khan Academy: Linear Algebra: Transposes of Sums and Inverses
Video explaining two properties of transpose matrices: that the transpose of the sum of two matrices is equivalent to the sum of the transpose of each matrix and that the inverse of the transpose of a matrix is equivalent to the...
Khan Academy
Khan Academy: Linear Algebra: Showing That a Transpose X a Is Invertible
A video lesson proving that the product of a matrix and its transpose is invertible if all of the columns of the originial matrix are linearly independent. [12:34]
Khan Academy
Khan Academy: Linear Algebra: Reduced Row Echelon Form 3
Video shows another example of using matrices and reduced row echelon form to simplify a system of 3 equations in 4 variables. Explains how to determine how many solutions the system will have by looking at the reduced row echelon form....
Khan Academy
Khan Academy: Linear Algebra: Reduced Row Echelon Form 2
Video shows example of using matrices and reduced row echelon form to solve a system of 3 equations in 3 variables. This video also appears in the strand Algebra: Matrices. [7:37]
Khan Academy
Khan Academy: Linear Algebra: Reduced Row Echelon Form 2
Video shows example of using matrices and reduced row echelon form to solve a system of 3 equations in 3 variables. This video also appears in the strand Algebra: Matrices. [7:37]
Khan Academy
Khan Academy: Linear Algebra: Inverting Matrices (Part 3)
Video shows how to determine the inverse of a 3 by 3 matrix using the Gauss-Jordan elimination method. This video also appears in the strand Algebra: Matrices. [13:35]
Khan Academy
Khan Academy: Linear Algebra: Example of Finding Matrix Inverse
A video lesson that works through a concrete example to find the inverse of a 3 x 3 matrix. The original matrix is augmented by the identity matrix and then put in reduced row echelon form. The result of the row operations on the...
Khan Academy
Khan Academy: Linear Algebra: Singular Matrices
Video explains why a matrix is singular if its determinant is 0. Illustrates that when a matrix equation is built with a singular matrix, then there are no solutions because the system it represents is that of two parallel lines. Shows...
Khan Academy
Khan Academy: Linear Algebra: Formula for 2 X 2 Inverse
A video lesson in which a formula is derived for finding the inverse of a 2 x 2 matrix. Addresses that a 2 x 2 matrix is only invertible if the determinant is not equal to 0. Defines the determinant and shows two examples of calculating...
Khan Academy
Khan Academy: Linear Algebra: Matrices to Solve a Vector Combination Problem
Demonstrates how to find the appropriate combination of two given vectors in order to obtain a third given vector. This is done by representing the problem with a single matrix equation and solving that equation. [14:20]
Khan Academy
Khan Academy: Linear Algebra: Inverse Matrix (Part 1)
Video first explains and gives examples of identity matrices. Then explains what an inverse matrix is and shows how to calculate the inverse of a 2x2 matrix. [14:14]
Sophia Learning
Sophia: Writing Systems of Equations With Augmented Matrices
This lesson demonstrates how to write systems of equations as augmented matrices. Students can watch a tutorial video and then take a quiz.
Virtual Nerd
Virtual Nerd: How Do You Subtract Matrices?
Instructional video illustrates the steps of subtracting matrices. [4:19]
Khan Academy
Khan Academy: Changing Coordinate Systems to Help Find a Transformation Matrix
Changing our coordinate system to find the transformation matrix with respect to standard coordinates
Khan Academy
Khan Academy: Change of Basis: Alternate Basis Transformation Matrix Example
Example of finding the transformation matrix for an alternate basis.
Khan Academy
Khan Academy: Matrices: Reduced Row Echelon Form 2
This video shows an example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form.
Khan Academy
Khan Academy: Invertible Change of Basis Matrix
Using an invertible change of basis matrix to go between different coordinate systems.
Khan Academy
Khan Academy: Linear Algebra: Inverting Matrices (Part 3)
Video shows using the Gauss-Jordan elimination method to determine the inverse of a 3 by 3 matrix. This video also appears in the strand Algebra: Matrices. [13:35]
Khan Academy
Khan Academy: Inverting Matrices: Inverting Matrices (Part 3)
Using Gauss-Jordan elimination to invert a 3x3 matrix.
Khan Academy
Khan Academy: Inverting Matrices: Inverting Matrices (Part 2)
Inverting a 3x3 matrix. This video includes using expansion of minors to determine the determinant and finding the matrix of cofactors and adjugate or adjoint matrix.
Khan Academy
Khan Academy: Linear Algebra: Singular Matrices
Video explains why a matrix is singular if its determinant is 0. Relates why the inverse does not exist to solving systems of linear equations and vector combinations. This video also appears in the strand Algebra: Matrices. [14:27]
Khan Academy
Khan Academy: Inverting Matrices: Singular Matrices
Video explains why a matrix is singular if its determinant is 0. Relates why the inverse does not exist to solving systems of linear equations and vector combinations.