How do you think about the column space and null space of a matrix visually? How do you think about the inverse of a matrix?

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Reaction-diffusion system: A hypothetical system in which multiple chemical substances diffuse through a defined space at different rates and react with one...

Your antivirus squad is up against a code that's hijacked your mainframe. What you've learned from other infected systems, right before they went dark, is that it likes to toy with antivirus agents in a very peculiar way— and you're the...

In this video Paul Andersen shows conceptual thinking in a mini-lesson on boundary and initial conditions within systems.

Boundary conditions - the dividing line between system and enviro
nment
Initial condition - the...

If patients seem to be unaware of their obvious conditions and symptoms, it might not be that they're in denial, but their brain might actually prevent them from realizing their disabilities.

Until recently, many teachers only got one word of feedback a year: "satisfactory." And with no feedback, no coaching, there's just no way to improve. Bill Gates suggests that even great teachers can get better with smart feedback -- and...

Thousands of languages thrive across the globe, yet modern speech technology -- with all of its benefits -- supports just over a hundred. Computational linguist Kalika Bali dreams of a day when technology acts as a bridge instead of a...

How do your pupils work and why do some substances make them dilate?

What if you never had to fill out paperwork again? In Estonia, this is a reality: citizens conduct nearly all public services online, from starting a business to voting from their laptops, thanks to the nation's ambitious post-Soviet...

So by the mid-90s the video game industry was once again booming and this attracted the attention of the Japanese electronics giant Sony. In 1994, Sony introduced their Playstation console which successfully coupled cutting edge...

In which John Green teaches you about Reconstruction. After the divisive, destructive Civil War, Abraham Lincoln had a plan to reconcile the country and make it whole again. Then he got shot, Andrew Johnson took over, and the...

From gigantic planets too close to their stars, to those in unfathomably wide orbits, astronomers have discovered seemingly impossible solar systems that shouldn’t exist at all. But they do.

SciShow News gives you some wet and weird developments from around the solar system, including new insights about what liquid lurks under the surface of Titan, and a sweaty comet that's been spotted on its way toward the sun.

So how do astronauts manage to pee and poop in microgravity? And what happens to all of their waste? Do you really want to know? If you do, the answers are inside!

What happens when a star eats its planets? Find out on today's Space Time Journal Club.

It was the dawn of 1863, and London's not-yet-opened subway system - the first of its kind in the world - had the city in an uproar. Most people thought the project, which cost more than 100 million dollars in today's money, would never...

Seema Bansal forged a path to public education reform for 15,000 schools in Haryana, India, by setting an ambitious goal: by 2020, 80 percent of children should have grade-level knowledge. She's looking to meet this goal by seeking...

What can you do when the wheels of justice don't turn fast enough? Or when they don't turn at all? Vivek Maru is working to transform the relationship between people and law, turning law from an abstraction or threat into something that...

In this video Paul Andersen shows conceptual thinking in a mini-lesson on systems as parts working together. TERMS System - a set of components (e.g. things) working together Part - a piece of an object or organism This progression is...

In this video Paul Andersen shows conceptual thinking in a mini-lesson on components and interactions within systems.

T
ERMS:
System - a set of components (e.g. things) workin
g together
Components - a part of
a larger...

You’ve seen dogs pant, but do you know why they do it? And is it true that dogs can’t sweat? Quick Questions has the answers!

Taxonomy is a powerful tool, and one that modern biology wouldn't be able to function without. But trying to shoehorn the messy, complicated web of interrelationships that is biology into neat boxes has resulted in a pretty messy tree of...

Paul Andersen explains a viral replication simulation that he created for his AP Biology class. He used Google docs to keep track of viral strains, Moodle messaging to pass the virus from student to student, and dice to generate...

The land of the free has become a legal minefield, says Philip K. Howard -- especially for teachers and doctors, whose work has been paralyzed by fear of suits. What's the answer? A lawyer himself, Howard has four propositions for...