This 13-minute video lesson shows how to calculate the null space of a matrix. [Linear Algebra playlist: Lesson 35 of 143]

This 12-minute video lesson discusses how to understand how the null space of a matrix relates to the linear independence of its column vectors. [Linear Algebra playlist: Lesson 36 of 143]

This 11-minute video lesson proves the "associative," "distributive," and "commutative" properties for vector dot products.

This 9-minute video lesson provides definitions of the vector dot product and vector length.

Students groups act as aerospace engineering teams competing to create linear equations to guide space shuttles safely through obstacles generated by a modeling game in level-based rounds. Each round provides a different configuration of the obstacle, which consists of two "gates." The obstacles are presented as asteroids or comets, and the linear equations as inputs into autopilot on board the shuttle. The winning group is the one that first generates the successful equations for all levels. The game is created via the programming software MATLAB, available as a free 30-day trial. The activity helps students make the connection between graphs and the real world. In this activity, they can see the path of a space shuttle modeled by a linear equation, as if they were looking from above.

Can you avoid the boulder field and land safely, just before your fuel runs out, as Neil Armstrong did in 1969? Our version of this classic video game accurately simulates the real motion of the lunar lander with the correct mass, thrust, fuel consumption rate, and lunar gravity. The real lunar lander is very hard to control.

Can you avoid the boulder field and land safely, just before your fuel runs out, as Neil Armstrong did in 1969? Our version of this classic video game accurately simulates the real motion of the lunar lander with the correct mass, thrust, fuel consumption rate, and lunar gravity. The real lunar lander is very hard to control.

This is a booklet containing 37 space science mathematical problems, several of which use authentic science data. The problems involve math skills such as unit conversions, geometry, trigonometry, algebra, graph analysis, vectors, scientific notation, and many others. Learners will use mathematics to explore science topics related to Earth's magnetic field, space weather, the Sun, and other related concepts. This booklet can be found on the Space Math@NASA website.

Students interested and engaged in game development careers are often students who are underprepared for direct entry into a Calculus sequence. Students who are hesitant to study computer science, are often interested and engaged in gaming. That’s what led to this set of activities; cloaking advanced mathematics to build confidence for teachers and students on a set of topics intimidating for educators and overwhelming for students.

We view this offering as a series of activities, rather than as a math book. Each activity includes short descriptions, examples, and most include teacher notes at activity end. Feel free to edit to support your students.

Learn about position, velocity, and acceleration in the "Arena of Pain". Use the green arrow to move the ball. Add more walls to the arena to make the game more difficult. Try to make a goal as fast as you can.

This is a problem-based learning adventure game that engages the player in the role of scientist, historian, and detective. At the beginning, the student is presented with a problem that must be solved. During the mission, students conduct field and laboratory investigations with the aid of the MedMyst characters. This mission can be played within one class period (approximately 30 to 45 minutes) and the knowledge gained from this mission will help students understand how infectious diseases are spread. This mission covers vectors, malaria, history of malaria, and immune system. Each mission is a self-contained problem and may be played without reliance on the other missions. Also available in Spanish.

In this unit you will see first how to convert vectors from geometric form, in terms of a magnitude and direction, to component form, and then how conversion in the opposite sense is accomplished. The ability to convert between these different forms of a vector is useful in certain problems involving displacement and velocity, as shown in Section‘_2, in which you will also work with bearings.

Try the new "Ladybug Motion 2D" simulation for the latest updated version. Learn about position, velocity, and acceleration vectors. Move the ball with the mouse or let the simulation move the ball in four types of motion (2 types of linear, simple harmonic, circle).

Try the new "Ladybug Motion 2D" simulation for the latest updated version. Learn about position, velocity, and acceleration vectors. Move the ball with the mouse or let the simulation move the ball in four types of motion (2 types of linear, simple harmonic, circle).

Mechanical energy is the most easily understood form of energy for students. When there is mechanical energy involved, something moves. Mechanical energy is a very important concept to understand. Engineers need to know what happens when something heavy falls from a long distance changing its potential energy into kinetic energy. Automotive engineers need to know what happens when cars crash into each other, and why they can do so much damage, even at low speeds! Our knowledge of mechanical energy is used to help design things like bridges, engines, cars, tools, parachutes, and even buildings! In this lesson, students will learn how the conservation of energy applies to impact situations such as a car crash or a falling object.

Learn about position, velocity, and acceleration graphs. Move the little man back and forth with the mouse and plot his motion. Set the position, velocity, or acceleration and let the simulation move the man for you.

Build your own system of heavenly bodies and watch the gravitational ballet. With this orbit simulator, you can set initial positions, velocities, and masses of 2, 3, or 4 bodies, and then see them orbit each other.