To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components …

To add the vectors (x₁,y₁) and (x₂,y₂), we add the corresponding components from each vector: (x₁+x₂,y₁+y₂). Here's a concrete example: the sum of (2,4) and (1,5) is (2+1,4+5), which is (3,9). There's also a nice graphical way to add vectors, and the two ways will always result in the same vector.

Describe a bivariate relationship's linearity, strength, and direction. In other words, plotting …

Describe a bivariate relationship's linearity, strength, and direction. In other words, plotting things that take two variables into consideration and trying to see whether there's a pattern with how they relate.

This video talka about what is easily one of the most fundamental …

This video talka about what is easily one of the most fundamental and profound concepts in statistics and maybe in all of mathematics. And that's the central limit theorem.

Sociology often looks at different age cohorts. A cohort is simply a …

Sociology often looks at different age cohorts. A cohort is simply a group of people, but here we're looking specifically at different age groups or generations, because these people all lived through the same certain events through a certain time that affected their lives similarly.

We've learned about matrix addition, matrix subtraction, matrix multiplication. So you might …

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 checks whether the commutative property applies for matrix multiplication. In other …

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 22-minute video lesson shows another example of a projection matrix. It …

This 22-minute video lesson shows another example of a projection matrix. It shows how to figure 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.

No restrictions on your remixing, redistributing, or making derivative works. Give credit to the author, as required.

Your remixing, redistributing, or making derivatives works comes with some restrictions, including how it is shared.

Your redistributing comes with some restrictions. Do not remix or make derivative works.

Most restrictive license type. Prohibits most uses, sharing, and any changes.

Copyrighted materials, available under Fair Use and the TEACH Act for US-based educators, or other custom arrangements. Go to the resource provider to see their individual restrictions.