Summary of 2. Elimination with Matrices.

00:00:00 - 00:45:00

This video discusses how to invert a matrix, or find the matrix which undoes the elimination process. The inverse matrix is found by adding 3 times Row 1 to Row 2.

• 00:00:00 In this video, Professor Lipson explains how elimination works, and how the first step is to multiply the equations by the right number. This will knock out the X part of equation two, and what will remain is the answer to the system.
• 00:05:00 The video explains the elimination process of a matrix, showing how to find the multipliers and pivots for each row and column. It concludes with an explanation of how to solve the resulting equation.
• 00:10:00 In this video, the presenter demonstrates how to solve a matrix equation by using three pivots. If the first number in the equation is zero, then the presenter recommends exchanging rows in order to get out of trouble. If the first number is not zero, then the presenter recommends exchanging for a lower equation in order to get a proper pivot.
• 00:15:00 In this video, the presenter discusses how to do elimination using matrices. First, they write the equations in standard form, then express the operations in matrices. They then carry the matrices along, but neglect to say what operations were performed. Finally, they express the results of the elimination in matrices again.
• 00:20:00 In this video, the author explains how matrix multiplication works. Row operations are also explained, and it is shown that matrix multiplication can result in a combination of the rows or columns of the matrices being multiplied.
• 00:25:00 In this video, the elimination process is explained in terms of matrix multiplication. The matrix E is used to solve a problem in which Row 1 of the original matrix is not to be changed. The next step is to subtract 1 from Row 1 of the original matrix, and that is expressed in matrix language as a matrix multiplication involving the matrix E.
• 00:30:00 This video covers the basics of matrix multiplication, including how to express an elimination matrix in terms of its constituent matrices. The video then goes on to explain how to create an elimination matrix using these concepts, and finishes with a demonstration.
• 00:35:00 In this video, the author explains the associative law for matrices, which states that matrices that have the same multiplication operator (that is, the same function that takes two rows and two columns and produces a new matrix with the same rows and columns) are automatically the same. This law is important because it allows for the easy calculation of matrices that have been specified in a simpler form.
• 00:40:00 The inverse of a matrix is a matrix that "undoes" the original matrix by subtracting its elements from each other. In this video, Professor Wessel notes that the inverse of a matrix is always a matrix that "undoes" the original matrix by subtracting its elements from each other. This is important to keep in mind when working with matrices, as the commutative law (which would allow for the matrix to be executed in a different order) is false in the real world.
• 00:45:00 This video teaches how to invert a matrix, or find the matrix which undoes the elimination process. The inverse matrix is found by adding 3 times Row 1 to Row 2.