Khan Academy: Linear Algebra: Introduction to the Null Space of a Matrix

Video reviews how to find the null space of a matrix using reduced row echelon form. Shows that the vectors of the null space are linearly independent and form a basis for the null space. Extends this to show how the nullspace can be...

Video reviews what the null space of a matrix is and how to calculate it, then relates it to linear independence. Shows that if the vectors are linearly independent then the null space is the zero vector. Also shows that if the null...

Video demonstrates how to calculate the null space of a matrix by creating a system of equations and using reduced row echelon form to solve and represent the null space by a linear combination of vectors and by the span of vectors. This...

Video first gives examples of finding the column space and null space of a matrix. Shows how to determine if the column space is a basis. Gives an example of finding the basis of the column space if the column space is not already a...

Video defining eigenvectors as scaled vectors and eigenvalues as their scale value and explaining their significance. Video references the example from a previous video about changing coordinate systems to make finding the transformation...

Video explains what linearly dependent vectors and linearly independent vectors are. Shows visual representations to help explain the concept and relates it to the span of the linear combination of the vectors. [15:46]

Video defining an orthonormal set as a set of vectors that all have the length of 1 and are orthogonal to each other. Using proof by contradiction, the set is proven to be linearly independent and can be considered an orthonormal basis....

Video first reviews what a function is. Explains what the identity function is and uses it to define what makes a function invertible. Shows that the inverse will be unique. This video also appears in the strand Algebra: Functions. [18:53]

Video reviews how to use vectors to define a line. Gives an intuitive sense of what a projection is, then explains step-by-step where the formula for projections comes from. Shows an example of calculating a vector projection. [14:37]

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]