Determine how much a linear transformation alters area. The seventh segment in a series of 15 makes the connection between the determinant and the scale factor of areas during a linear transformation. The video goes on to explain the...

Bring it all to three dimensions. The short video points out that the discussion in the previous presentations in two dimensions also holds true for three dimensions. The sixth video in the series of 15 specifically makes the...

The dot product of two matrices is a number on the number line, its transformation. The resource presents the dot product as a linear transformation from two dimensions to one dimension. The video uses the numerical and graphical...

But what happens if the matrix is not square? The ninth video in a series of 15 serves as a footnote to discuss non-square matrices. The resource presents them as transformations between two and three dimensions. The presentation...

How much wood would ...? The quick video uses a linear equation to determine the size of a bookshelf given a diagram of the shelves and the amount of wood to use. Scholars see how to set up the equation and solve it to determine the...

First, Sal defines consistent and inconsistent equations. He then evaluates a system of linear equations to determine if they are consistent or not. This resource isobviousr and would be a wonderful video to show before a test or at an...

Use one-dimensional calculations to make them two-dimensional. An application question provides a perimeter and a relationship between the length and width of a rectangle. The video tutorial demonstrates how to write an equation for...

Matrix, matrices, what? The instructor demonstrates how to set up a matrix and explains the rows and columns, the dimensions. There are many uses for matrices and this is just the beginning.

No, matrices are not what mathematicians sleep on. Lesson begins with identifying the dimensions of matrices then moves on to multiply them. It also provides guided practice problems that get progressively more complex.

Soil may seem flat, but it has dimension. A quick video lesson walks learners through the different dimensions of a sample of soil. Beginning with the linear measurements, the instruction describes the area and volume calculations as...

Matrix, matrices, what? The instructor demonstrates how to set up a matrix and explains the rows and columns. There are many uses for matrices and this is just the beginning.

If one meter is 100 centimeters, how many square centimeters is equal to one square meter? Hint: the answer isn't 100! How many pupils make this mistake? A video lesson calculates the conversion factor of the common metric area units....

A half-hour introductory video on mechanics and the metric system was produced with beginning physicists in mind. Note-taking guides are provided, in addition to a follow-up metric worksheet. For the lab, learners construct paper frogs....

Solve a collision of balls in two dimensions problem using the conservations of momentum in this video. Video gives a step-by-step explanation of how to solve the problem to figure out what direction and velocity the balls travel after...

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 explains what a linear combination is and gives a concrete example of a linear combination of two vectors in two dimensions. Linear combinations are then extended to introduce spans of vectors. Shows a proof that two non-parallel...

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]

Video shows example of multiplying matrices. Includes explanation of the dimensions needed in order for matrices to be able to be multiplied. Connects to the composition of linear transformations. This video also appears in the strand...

Video explains what a basis for a vector subspace is and its criteria: the vectors must span the subspace and be linearly independent. Also gives an informal definition of basis as the minimum set of vectors that spans the subspace....

Video first reviews how to find the basis for the column space of a matrix using the reduced row echelon form. Proves that the basis for the column space using the reduced row echelon form method spans the column space. Uses this and the...

Video gives examples of vector addition, graphing vectors, multiplying vectors by a scalar and vector subtraction using vectors in R2 and extends to vectors in other dimensions. [25:33]

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 explains what a linear combination is and gives a concrete example of a linear combination of two vectors in two dimensions. Linear combinations are then extended to introduce spans of vectors. Shows a proof that two non-parallel...