Linear Systems: Applications of Linear Algebra to Differential Equations

Learners find the common point of a linear and quadratic system given a graph of the system. Then they find a specific point located only on the parabola.

Put all that algebra learning to use! Using algebraic strategies, learners solve three-variable systems. They then use the three-variable systems to write a quadratic equation given three points on the parabola.

Expand on learners' understanding of quadratic-linear systems. Building on the graphic understanding developed in the previous lesson plan, pupils learn algebraic methods of solving the systems. 

Explore methods for solving linear systems with your classes and introduce learners to using matrices as a viable method. Scholars are able to recognize situations where matrices are the efficient method of solving. Application questions...

Trying to find a linear transformation is like finding a needle in a haystack. The second lesson in the series of 32 continues to explore the concept of linearity started in the first lesson. The class explores trigonometric, rational,...

Not all linear functions are linear transformations — show your class the difference. The first lesson plan in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations...

A brief presentation with laser-like focus, this video talks young mathematicians through the mechanics of simplifying algebraic fractions by factoring trinomials. While the factoring itself is assumed to be a mastered skill, the steps...

Take your class through the mechanics of simplifying algebraic fractions by factoring trinomials. Though the steps for factoring are assumed known, the process of identifying and canceling common factors are detailed with care and...

Here is a challenging motion problem about two different length trains and how long it takes them to pass each other going in the same direction and opposite directions. At first glance, there doesnÕt seem to be enough information given...

What does it mean for two vectors to be linearly independent? The resource presents the basics of basis vectors and linear combinations. The third video in the 15-part series provides a definition of linear independence in terms of the...