Introduction to experiment design. Explanatory and response variables. Control and treatment groups.
We've learned about matrix addition, matrix subtraction, matrix multiplication. So you might be wondering, is there the equivalent of matrix division? And before we get into that, let me introduce some concepts to you. And then we'll see that there is something that maybe isn't exactly division, but it's analogous to it.
Sal introduces the famous and super important Pythagorean theorem! This lesson includes an introduction video followed by examples and practice problems involving finding the hypotenuse, finding a side, finding area of an isosceles triangle, and determining if a triangle is a right triangle. It is followed by a unit on Pythagorean theorem applications.
Sal checks whether the commutative property applies for matrix multiplication. In other words, he checks whether for any two matrices A and B, A*B=B*A (the answer is NO, by the way). Created by Sal Khan.
This 16-minute video lesson shows that a projection onto a subspace is a linear transformation. [Linear Algebra playlist: Lesson 110 of 143]
This 14-minute video lesson shows how to determine the equation for a plane in R3 using a point on the plane and a normal vector.
This 25-minute video lesson introduces the idea of an angle between two vectors.
This 19-minute video lesson provides dot and cross product comparison and Intuition.
This 27-minute video lesson provides an example using the orthogonal change-of-basis matrix to find the transformation matrix. [Linear Algebra playlist: Lesson 128 of 143]
This 17-minute video lesson shows how to express a projection on to a line as a Matrix Vector prod. [Linear Algebra playlist: Lesson 61 of 143]
This 15-minute video lesson shows how to find the eigenvectors and eigenspaces of a 2x2 matrix. [Linear Algebra playlist: Lesson 136 of 143]
This 12-minute video lesson provides an introduction to the null space of a matrix and shows that the null space of a matrix is a valid subspace. [Linear Algebra playlist: Lesson 34 of 143]
This 18-minute video lesson shows how to solve a system of linear equations by putting an augmented matrix into reduced row echelon form. [Linear Algebra playlist: Lesson 30 of 143]
This 12-minute video lesson provides another example of solving a system of linear equations by putting an augmented matrix into reduced row echelon form. [Linear Algebra playlist: Lesson 32 of 143]
This 10-minute video lesson shows how to figure out a normal vector to a plane from its equation. [Linear Algebra playlist: Lesson 141 of 143]
This 13-minute video lesson shows how to calculate the null space of a matrix. [Linear Algebra playlist: Lesson 35 of 143]
This 12-minute video lesson discusses how to understand how the null space of a matrix relates to the linear independence of its column vectors. [Linear Algebra playlist: Lesson 36 of 143]
This 12-minute video lesson finds that the orthogonal complement of the orthogonal complement of V is V. [Linear Algebra playlist: Lesson 103 of 143]
This 11-minute video lesson shows that orthogonal matrices preserve angles and lengths. [Linear Algebra playlist: Lesson 129 of 143]
This 17-minute vidoe lesson shows proof of the Cauchy-Schwarz Inequality.