Khan Academy
Khan Academy: Linear Algebra: Transpose of a Matrix
Video explaining that the transpose of a matrix is created by switching rows and columns. The idea is shown abstractly and specifically with 2x2 matrix and 4x3 matrix. Also shows that the transpose of a transpose is the original matrix....
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: Transpose of a Vector
Video demonstrating that the dot product of two vectors is equivalent to the matrix product of the transpose of the first vector times the second vector. Uses this idea to show that the dot product of a matrix-vector product and another...
Khan Academy
Khan Academy: Linear Algebra: Distributive Property of Matrix Products
Video shows that the distributive property is true for multiplying matrices. [9:52]
Khan Academy
Khan Academy: Linear Algebra: Transpose of a Matrix Product
Video demonstrating that the transpose of the product of two matrices is equivalent to the product of their transposes in reversed order. [8:50]
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: Matrix Vector Products
Video starts with reviewing matrix notation. Defines multiplying a matrix by a vector and shows examples. Shows how the matrix-vector products can be interpreted as the dot product of column vectors with a matrix or as a weighted linear...
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....
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: Linear Algebra: More on Linear Independence
Video expands the examples of linearly independent and linearly dependent vectors shown in the previous video to give a formal definition of linearly dependent vectors. Shows a proof of the definition and then gives an example of using...
Khan Academy
Khan Academy: Change of Basis: Alternate Basis Transformation Matrix Part 2
Showing that the transformation matrix with respect to basis B actually works. Brief point on why someone would want to operate in a different basis to begin with.
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: Invertible Change of Basis Matrix
Using an invertible change of basis matrix to go between different coordinate systems.
Khan Academy
Khan Academy: Basic Matrix Operations: Matrix Addition and Subtraction
Adding and subtracting matrices.
Khan Academy
Khan Academy: Calculating Matrix of Minors and Cofactor Matrix
Inverting a 3x3 matrix then calculate the matrix of minors and the cofactor matrix.
Sophia Learning
Sophia: Using Elementary Row Operations to Solve for Systems of Equations
This video lesson demonstrates how to solve a system of linear equations by using matrix row operations. Students can check their understanding with an assessment.
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....
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....
Khan Academy
Khan Academy: More on Matrix Addition and Scalar Multiplication
Video shows 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.
Khan Academy
Khan Academy: Markov Chains
By Samuel Cryan. Markov Chains are a fascinating mathematical trick that is able to find meaning in large clumps of disorganized data. Watch and learn what the heck Markov Chains are, and how Google uses them to rank the webpages out there.
Khan Academy
Khan Academy: Alternate Basis Transformation Matrix Example Part 2
Showing that the transformation matrix with respect to basis B actually works. Brief point on why someone would want to operate in a different basis to begin with.
Khan Academy
Khan Academy: Alternate Basis Transformation Matrix Example
Example of finding the transformation matrix for an alternate basis.