yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Finding area of figure after transformation using determinant | Matrices | Khan Academy


2m read
·Nov 10, 2024

We're told to consider this matrix transformation. This is a matrix that you can use, it represents a transformation on the entire coordinate plane. Then they tell us that the transformation is performed on the following rectangle. So, this is the rectangle before the transformation. They say, what is the area of the image of the rectangle under this transformation? The image of the rectangle is what the rectangle becomes after the transformation.

So pause this video and see if you can answer that before we work through it on our own. All right, so the main thing to realize is if we have a matrix transformation or a transformation matrix like this, if we take the absolute value of its determinant, that value tells us how much that transformation scales up areas of figures.

So let's just do that. Let's evaluate the absolute value of the determinant here. The absolute value of the determinant would be the absolute value of five times eight minus nine times four. Remember, for a two by two matrix, the determinant is just this times this minus this times that. That's going to be the absolute value of 40 minus 36, which is just the absolute value of 4, which is just going to be equal to 4.

So, this tells us that this transformation will scale up area by a factor of 4. So what's the area before the transformation? Well, we can see that this is, let's see, it's 5 units tall and it is 7 units wide. So this has an area of 35 square units pre-transformation.

So post-transformation, we just multiply it by the absolute value of the determinant to get, let's see, 4 times 35, which is 140 square units. And we're done.

More Articles

View All
Keeping the Inuit Way of Life Alive in a Changing World | Short Film Showcase
Inuit were born to be outside. My earliest memories of growing up with my family were connected to the land, using dog-teams, skin tents. Hi ox he lived on the land. You took what you needed. We didn’t have electric power; we didn’t have modern convenien…
Dan Siroker at Startup School 2013
Thank you. Uh, I have the privilege of saying this is my sixth Startup School, uh, and, uh, the first time as a presenter. Today, I’m going to be sharing with you what I would have wanted to hear the first five times, uh, while I was sitting in your seat…
Defending Marine Wildlife | Explorer
NARRATOR: It’s the Sam Simon and its crew that are confronting the issues here head on. Of course, their day was a bit frustrating when you see this overwhelming amount of nets that’s out there, that there’s still the fishermen going out and laying more n…
GameStop's Final Blow to the Short Sellers
So as we’ve been following over the last couple of months, Gamestop shares have literally been flying all over the place in the aftermath of the Reddit-fueled short squeeze that happened at the end of January. Over the past couple of months, myself and Ha…
Why I'm Selling My Stocks
What’s up? Grandma’s guys here. So yes, to Tony, you saw is true, and I want to be completely transparent because it’s that time of the year to start cashing out of the stock market again. Now I know what you’re thinking, but Grant, you said that you woul…
This TRANSPARENT ENGINE is Fascinating (How Engines Work) - Smarter Every Day 292
Where should the camera be? Oh, wherever. [Smashed the Gas] HOLY…. ENGINE ROARS Hey, it’s me, Destin. Welcome back to Smart Every Day. We have explored internal combustion engines on this channel, and I think they’re amazing. In the past, we visited a You…