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 shows how to find the basis and dimension of the column space by finding its reduced row echelon form and using the columns corresponding to the pivot columns as the basis. Explains that rank is the dimension of the column space....

Video shows proof that any basis of a particular subspace has the same number of elements. Leads up to give the definition of dimension. This video also appears in the strand Algebra: Matrices. [21:25]

This lesson will explore the definition, depiction, and location of three dimensional objects. It is 7 of 7 in the series titled "Two Dimensions."

This lesson provides real-world examples that demonstrate how to organize data into matrices. It is 4 of 5 in the series titled "Using Matrices to Organize Data." [8:40]

Through this lesson, you'll learn the definition, depiction, and location of zero dimensions and zero dimensional objects. It is 6 of 7 in the series titled "Zero Dimensions."

In school, we learn about shapes with sides and edges - but there are weird shapes out there (beyond our 3 dimensions) that defy our normal idea of geometry. QuanQuan and Jenny explain, knit, and 3D print their way through trippy shapes!...

The scientists from Crash Course Physics introduce the ideas of vectors and scalars so we can better understand how to figure out motion in 2 Dimensions. [10:05]

Here's a nifty word problem in which we find the dimensions of a garden given only the perimeter. Sal Khan creates an equation to solve. [2:02]