Numerical Analysis: Discrete Least Squares

In this least squares activity, students solve 6 different problems that include the least squares of numbers. First, they plot 3 points on the axes shown and draw in their best approximating line. Then, students estimate the slope and...

In this least squares approximation worksheet, students use linear algebra to find the least square error and the equation of a line for given points. They find the equation of a parabola through provided points. This four-page...

In this least squares approximation worksheet, students determine the number of solutions a given linear system has. They find the least square error and the equation of a line of best fit for a set of three points. Students find the...

In this least squares worksheet, students solve 3 different problems that include determining the least squares of equations. First, they use the data given in the table to write out the normal equations a system of 2 equations in 2...

In this numerical analysis worksheet, students solve systems of non-linear equations. Examples and explanation are provided. This two-page worksheet contains approximately three problems.

In this linear system worksheet, learners explore the characteristics of given matrices. They multiply matrices and determine pivots and multiply solutions. This four-page worksheet contains approximately seven problems.

In this determinant activity, students find the determinants of matrices. They identify patterns and their relationship to the canonical matrix. This two-page activity contains approximately nine problems, as well as examples and...

In this least square regression worksheet, students find solutions to given linear systems. They draw pictures, draw a vector and prove the solution. This two-page worksheet contains eleven problems, with some examples and explanations.

In this basis and dimension activity, students explore vector spaces associated with rectangular matrices. The two-page activity contains approximately 20 short answer questions.

Summarizing his thoughts on creating the last few videos on the weaknesses of the fractional reserve, Sal goes on to explain why he believes the nature of this system is "disingenuous. " This leads to a discussion that contextualizes the...