TedTest

From the Ted Talk by Bill Shillito: How to organize, add and multiply matrices

Unscramble the Blue Letters

By now, I'm sure you know that in just about anything you do in life, you need numbers. In particular, though, some flides don't just need a few numbers, they need lots of them. How do you keep track of all those numbers? Well, meanaihacttmis daintg back as early as ancient cihna came up with a way to represent arrays of many numbers at once. Nowadays we call such an array a "matrix," and many of them hanging out together, "matrices". Matrices are everywhere. They are all around us, even now in this very room. Sorry, let's get back on trcak. Matrices really are everywhere, though. They are used in business, economics, ctpphryraogy, physics, eloecrintcs, and computer graphics. One reason matrices are so cool is that we can pack so much information into them and then turn a huge series of different problems into one single problem. So, to use matrices, we need to learn how they work. It turns out, you can treat matrices just like regular numbers. You can add them, subtract them, even multiply them. You can't divide them, but that's a riabbt hole of its own. Adding matrices is pretty simple. All you have to do is add the corresponding entries in the order they come. So the first entries get added together, the second entries, the third, all the way down. Of course, your matrices have to be the same size, but that's pretty intuitive anyway. You can also multiply the whole matrix by a number, called a scalar. Just multiply every entry by that number. But wait, there's more! You can actually mlluptiy one matrix by another matrix. It's not like adding them, though, where you do it etrny by entry. It's more unique and pretty cool once you get the hang of it. Here's how it works. Let's say you have two macrteis. Let's make them both two by two, meaning two rows by two columns. wtire the first matrix to the left and the second matrix goes next to it and translated up a bit, kind of like we are making a table. The pucrodt we get when we multiply the matrices together will go right between them. We'll also draw some gridlines to help us along. Now, look at the first row of the first matrix and the first column of the second matrix. See how there's two numbers in each? Multiply the first number in the row by the first numebr in the column: 1 times 2 is 2. Now do the next ones: 3 times 3 is 9. Now add them up: 2 plus 9 is 11. Let's put that number in the top-left position so that it matches up with the rows and columns we used to get it. See how that works? You can do the same thing to get the other enertis. -4 plus 0 is -4. 4 plus -3 is 1. -8 plus 0 is -8. So, here's your answer. Not all that bad, is it? There's one catch, though. Just like with addition, your matrices have to be the right size. Look at these two matrices. 2 times 8 is 16. 3 times 4 is 12. 3 tmies wait a minute, there are no more rows in the second matrix. We ran out of room. So, these matrices can't be mtiluilped. The number of columns in the first mitarx has to be the same as the number of rows in the second matrix. As long as you're cfauerl to match up your dimensions right, though, it's ptrety easy. Understanding matrix mlclaiuiittpon is just the beginning, by the way. There's so much you can do with them. For example, let's say you want to encrypt a secret message. Let's say it's "Math rules". Though, why anybody would want to keep this a secret is beyond me. Letting numbers stand for letters, you can put the numbers in a matrix and then an encryption key in another. Multiply them together and you've got a new encoded matrix. The only way to decode the new matrix and read the message is to have the key, that second matrix. There's even a branch of mathematics that uses matrices constantly, caelld Linear Algebra. If you ever get a chance to study lienar Algebra, do it, it's pretty aewmsoe. But just remember, once you know how to use matrices, you can do pretty much anything.

Open Cloze

By now, I'm sure you know that in just about anything you do in life, you need numbers. In particular, though, some ______ don't just need a few numbers, they need lots of them. How do you keep track of all those numbers? Well, ______________ ______ back as early as ancient _____ came up with a way to represent arrays of many numbers at once. Nowadays we call such an array a "matrix," and many of them hanging out together, "matrices". Matrices are everywhere. They are all around us, even now in this very room. Sorry, let's get back on _____. Matrices really are everywhere, though. They are used in business, economics, ____________, physics, ___________, and computer graphics. One reason matrices are so cool is that we can pack so much information into them and then turn a huge series of different problems into one single problem. So, to use matrices, we need to learn how they work. It turns out, you can treat matrices just like regular numbers. You can add them, subtract them, even multiply them. You can't divide them, but that's a ______ hole of its own. Adding matrices is pretty simple. All you have to do is add the corresponding entries in the order they come. So the first entries get added together, the second entries, the third, all the way down. Of course, your matrices have to be the same size, but that's pretty intuitive anyway. You can also multiply the whole matrix by a number, called a scalar. Just multiply every entry by that number. But wait, there's more! You can actually ________ one matrix by another matrix. It's not like adding them, though, where you do it _____ by entry. It's more unique and pretty cool once you get the hang of it. Here's how it works. Let's say you have two ________. Let's make them both two by two, meaning two rows by two columns. _____ the first matrix to the left and the second matrix goes next to it and translated up a bit, kind of like we are making a table. The _______ we get when we multiply the matrices together will go right between them. We'll also draw some gridlines to help us along. Now, look at the first row of the first matrix and the first column of the second matrix. See how there's two numbers in each? Multiply the first number in the row by the first ______ in the column: 1 times 2 is 2. Now do the next ones: 3 times 3 is 9. Now add them up: 2 plus 9 is 11. Let's put that number in the top-left position so that it matches up with the rows and columns we used to get it. See how that works? You can do the same thing to get the other _______. -4 plus 0 is -4. 4 plus -3 is 1. -8 plus 0 is -8. So, here's your answer. Not all that bad, is it? There's one catch, though. Just like with addition, your matrices have to be the right size. Look at these two matrices. 2 times 8 is 16. 3 times 4 is 12. 3 _____ wait a minute, there are no more rows in the second matrix. We ran out of room. So, these matrices can't be __________. The number of columns in the first ______ has to be the same as the number of rows in the second matrix. As long as you're _______ to match up your dimensions right, though, it's ______ easy. Understanding matrix ______________ is just the beginning, by the way. There's so much you can do with them. For example, let's say you want to encrypt a secret message. Let's say it's "Math rules". Though, why anybody would want to keep this a secret is beyond me. Letting numbers stand for letters, you can put the numbers in a matrix and then an encryption key in another. Multiply them together and you've got a new encoded matrix. The only way to decode the new matrix and read the message is to have the key, that second matrix. There's even a branch of mathematics that uses matrices constantly, ______ Linear Algebra. If you ever get a chance to study ______ Algebra, do it, it's pretty _______. But just remember, once you know how to use matrices, you can do pretty much anything.

Solution

matrix
linear
entries
cryptography
entry
matrices
called
write
careful
number
awesome
track
fields
product
pretty
times
dating
multiply
electronics
china
multiplication
multiplied
mathematicians
rabbit

Original Text

By now, I'm sure you know that in just about anything you do in life, you need numbers. In particular, though, some fields don't just need a few numbers, they need lots of them. How do you keep track of all those numbers? Well, mathematicians dating back as early as ancient China came up with a way to represent arrays of many numbers at once. Nowadays we call such an array a "matrix," and many of them hanging out together, "matrices". Matrices are everywhere. They are all around us, even now in this very room. Sorry, let's get back on track. Matrices really are everywhere, though. They are used in business, economics, cryptography, physics, electronics, and computer graphics. One reason matrices are so cool is that we can pack so much information into them and then turn a huge series of different problems into one single problem. So, to use matrices, we need to learn how they work. It turns out, you can treat matrices just like regular numbers. You can add them, subtract them, even multiply them. You can't divide them, but that's a rabbit hole of its own. Adding matrices is pretty simple. All you have to do is add the corresponding entries in the order they come. So the first entries get added together, the second entries, the third, all the way down. Of course, your matrices have to be the same size, but that's pretty intuitive anyway. You can also multiply the whole matrix by a number, called a scalar. Just multiply every entry by that number. But wait, there's more! You can actually multiply one matrix by another matrix. It's not like adding them, though, where you do it entry by entry. It's more unique and pretty cool once you get the hang of it. Here's how it works. Let's say you have two matrices. Let's make them both two by two, meaning two rows by two columns. Write the first matrix to the left and the second matrix goes next to it and translated up a bit, kind of like we are making a table. The product we get when we multiply the matrices together will go right between them. We'll also draw some gridlines to help us along. Now, look at the first row of the first matrix and the first column of the second matrix. See how there's two numbers in each? Multiply the first number in the row by the first number in the column: 1 times 2 is 2. Now do the next ones: 3 times 3 is 9. Now add them up: 2 plus 9 is 11. Let's put that number in the top-left position so that it matches up with the rows and columns we used to get it. See how that works? You can do the same thing to get the other entries. -4 plus 0 is -4. 4 plus -3 is 1. -8 plus 0 is -8. So, here's your answer. Not all that bad, is it? There's one catch, though. Just like with addition, your matrices have to be the right size. Look at these two matrices. 2 times 8 is 16. 3 times 4 is 12. 3 times wait a minute, there are no more rows in the second matrix. We ran out of room. So, these matrices can't be multiplied. The number of columns in the first matrix has to be the same as the number of rows in the second matrix. As long as you're careful to match up your dimensions right, though, it's pretty easy. Understanding matrix multiplication is just the beginning, by the way. There's so much you can do with them. For example, let's say you want to encrypt a secret message. Let's say it's "Math rules". Though, why anybody would want to keep this a secret is beyond me. Letting numbers stand for letters, you can put the numbers in a matrix and then an encryption key in another. Multiply them together and you've got a new encoded matrix. The only way to decode the new matrix and read the message is to have the key, that second matrix. There's even a branch of mathematics that uses matrices constantly, called Linear Algebra. If you ever get a chance to study Linear Algebra, do it, it's pretty awesome. But just remember, once you know how to use matrices, you can do pretty much anything.

Frequently Occurring Word Combinations

Important Words

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