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Inverse Matrices 689 Views


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Description:

Neo, we're not in the Matrix anymore.

Language:
English Language

Transcript

00:04

Inverse matrices a'la Shmoop!

00:06

After an unfortunate drugstore accident there's a hole in the space-time continuum…[Man dropping a substance and creating a green hole in the drug store]

00:11

…Joel, the pharmacist’s assistant, finds himself inside a matrix.

00:16

Not THE Matrix; just a matrix. [Joel trapped inside the matrix]

00:18

Specifically, a two by two matrix with the values 1, 3, -2, and, -1.

00:24

Suddenly… JOEL, IF YOU STAY

00:27

HERE TOO LONG…

00:29

…THE HOLE IN THE SPACE-TIME CONTINUUM WILL CLOSE, TRAPPING YOU HERE FOREVER. [Man wearing sunglasses ordering Joel to leave the space time continuum]

00:33

THE ONLY WAY TO ESCAPE THIS MATRIX IS TO INVERT IT.

00:38

ONCE THE MATRIX IS INVERTED, YOU WILL FALL BACK INTO YOUR OWN DIMENSION.

00:42

How does Joel invert this matrix so he can get back to the right dimension? [Question on chalkboard asking Joel how can get back to his own dimension]

00:47

First he tries turning the matrix upside down.

00:49

That doesn’t work.

00:51

Next he tries reversing the order of the numbers. [Joel re-ordering the numbers in the equation]

00:53

Nope.

00:54

Let’s help him out with some basics.

00:55

There’s a three-step trick to finding the inverse of a two by two matrix.

00:59

First, we find the determinant, which we can do with this formula: a times d minus b times [A finger finding the determinant of the matrices]

01:06

c.

01:07

We can see that a equals 1, b equals 3, c equals negative 2, and d equals negative 1…

01:14

…so plugging this into our determinant formula, we see that 1 times negative 1 minus 3 times [numbers plugged into the determinant formula]

01:21

negative 2… gives us negative 1 plus 6… or 5.

01:26

The next step in finding the inverse is to switch the positions of a and d…[A and B are switched in the formula]

01:30

…and switch the signs of c and b.

01:34

So if we look back to our matrix, a and d switch places...

01:38

…so the top left corner of the matrix becomes negative 1 and the bottom right corner becomes

01:44

1.

01:45

Then we switch the signs of c and b, so 3 becomes negative 3 and negative 2 becomes [C and B signs switched]

01:51

positive 2.

01:53

For the final step, take that mixed-up matrix and multiply the whole thing by 1 over the [A step of a staircase of the final step in locating the determinant]

01:58

determinant, which is 5.

02:01

though we get -1/5, -3/5, 2/5, and 1/5.

02:08

Inverse matrix achieved.

02:09

BACK TO YOUR OWN DIMENSION, PHARMACIST. Off you go [Man ordering Joel goes back to his dimension and Joel appears back in the pharmacy]

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