Corbett Maths
Column Vectors
Column right! Using visual representations, a short video introduces the concept of column vectors. Next, the resource shows how adding two vectors end-to-end is simplified by adding the components in the column vector. The presentation...
3Blue1Brown
Essence of Linear Algebra Preview
Make connections with linear algebra. The video introduces the concept of linear algebra and its geometric underpinnings. The resource makes the case that a complete understanding of linear algebra topics should include geometric...
Brightstorm
Square Matrices - Concept
No, matrices are not what mathematicians sleep on. Lesson begins with identifying the dimensions of matrices then moves on to multiply them. It also provides guided practice problems that get progressively more complex.
Khan Academy
Khan Academy: Algebra: Matrices: Matrix Multiplication (Part 2)
This lesson goes through three examples of matrix multiplication. Explains how the dimensions of matrices affect whether or not the matrices can be multiplied, how to determine if they can be multiplied, and what size the resulting...
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 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: 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: Matrix Product Examples
Video shows example of multiplying matrices. Includes explanation of the dimensions needed in order for matrices to be able to be multiplied. Connects to the composition of linear transformations. This video also appears in the strand...
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: More on Matrix Addition and Scalar Multiplication
Video reviews what was shown in the previous video that the sum of two linear transformations is the sum of their transformation matrices and the scalar multiple of a transformation is the scalar multiple of the transformation matrix....
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.
Khan Academy
Khan Academy: Algebra: Matrices: Matrix Multiplication (Part 1)
A lesson on multiplying matrices. Gives an example of two 2 X 2 matrices being multiplied. Illustrates that matrix multiplication is not commutative and that the order in which matrices are multiplied is important. [13:41]
Virtual Nerd
Virtual Nerd: How Do You Subtract Matrices?
Instructional video illustrates the steps of subtracting matrices. [4:19]
Virtual Nerd
Virtual Nerd: How Do You Add and Subtract Matrices With Fractions and Decimals?
Follow along with this tutorial to get some practice adding and subtracting matrices using decimals and fractions. [4:42]
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: 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.