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: 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.
Khan Academy
Khan Academy: Change of Basis: Coordinates With Respect to a Basis
Understanding alternate coordinate systems.
Khan Academy
Khan Academy: More Determinant Depth: Determinant When Row Is Added
A video lesson explaining the determinant rule for the very special case when three matrices are identical except for one row, and that row of the third matrix is the sum of those rows in the other two matrices.
Khan Academy
Khan Academy: More Determinant Depth: Upper Triangular Determinant
A video lesson proving that the determinant of an upper triangular matrix is the product of the all of the entries along the main diagonal
Khan Academy
Khan Academy: More Determinant Depth: (Correction) Scalar Multiplication of Row
Correction of last video showing that the determinant when one row is multiplied by a scalar is equal to the scalar times the determinant
Khan Academy
Khan Academy: Simplifying Conditions for Invertibility
A video lesson explaining that a transformation matrix is invertible if and only if it is a square identity matrix in reduced row echelon form.
Khan Academy
Khan Academy: Finding Inverses of Matrices: Rule of Sarrus of Determinants
A alternative "short cut" for calculating 3x3 determinants (Rule of Sarrus)
Khan Academy
Khan Academy: Finding the Determinant of a 3 X3 Matrix Method 2
This video shows how to find the determinant of a thre by three matrix.
Khan Academy
Khan Academy: Finding the Determinant of a 3 X3 Matrix Method 1
A video showing how to find the determinant of a 3 x 3 matrix.
Khan Academy
Khan Academy: Inverting Matrices: Inverse of a 2 X2 Matrix
Example of calculating the inverse of a 2x2 matrix.
Khan Academy
Khan Academy: Inverting 3 X3 Part 2: Determinant and Adjugate of a Matrix
This is part two of video about 3x3 matrix inversion.
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: Inverting Matrices: Finding the Determinant of a 2 X2 Matrix
Hint for finding the determinant of a 2x2 matrix,
Khan Academy
Khan Academy: Precalculus: Visual Representation of Transformation From Matrix
Demonstrates how to represent a 2x2 matrix transformation on a plane. [6:08]
Study Pug
Study Pug: Absolute Value Functions
Absolute value is basically the distance between "number" and "zero" on a number line. You will learn more about this concept in this video. You will also learn how to express absolute value functions as piecewise functions. [10:47]
Khan Academy
Khan Academy: Another Example of a Projection Matrix
Figuring out the transformation matrix for a projection onto a subspace by figuring out the matrix for the projection onto the subspace's orthogonal complement first.
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.
Sophia Learning
Sophia: Using Determinants to Classify 2x2 Matrices
This lesson demonstrates how the determinant of a 2x2 matrix can be used to tell whether or not the matrix represents a dependent linear system, an inconsistent linear system, or neither.
Sophia Learning
Sophia: Using Determinants to Classify Systems of 3x3 Matrices
This lesson demonstrates how the determinant of a 3x3 matrix can be used to tell whether or not the matrix represents a dependent linear system, an inconsistent linear system, or neither.
Sophia Learning
Sophia: Using Determinants to Classify 3x3 Matrices: Lesson 4
This lesson demonstrates how the determinant of a 3x3 matrix can be used to tell whether or not the matrix represents a dependent linear system, an inconsistent linear system, or neither.
Sophia Learning
Sophia: Using Determinants to Classify Systems of 2x2 Matrices
This lesson demonstrates how the determinant of a 2x2 matrix can be used to tell whether or not the matrix represents a dependent linear system, an inconsistent linear system, or neither.