Transpose of a matrix

Hey guys, I'm going to do a quick lesson without a video. This lesson will be on finding the transpose of a matrix. This is so simple, I can't justify the time, effort, and space to make a video for it. However, I want to post it anyway, because I'll be honest with you: I had totally forgotten what a transpose of a matrix even was until I started studying it. If I hadn't figured it out, I would have been scared and probably taken a wild guess at an answer on the exam and lost easy points. But you won't have to do that, because I'm going to teach you what it is and you'll get the question right. Ready?

Here it is: the transpose of a matrix is just another matrix you create by taking each row and writing it down as a corresponding column.

Put another way, in the transpose of Matrix A, the i-th row becomes the i-th column. Make sense?

Here's an example: say we want to find the transpose of the following matrix:



| 1 2 |
| 3 4 |

So we take Row 1 and make it Column 1:

| 1
| 2

And we take Row 2 and make it Column 2:

| 1 3 |
| 2 4 |

Boom shaka laka! All there is to it.

It's so easy, they'll probably give you a matrix that's all jacked up on the exam so you can't put it into your calculator. They'll want you to find the transpose of something like this:

| 1 8 2 4 9 0 2 3 |
| 4 8 9 1 0 0 9 2 |

If you didn't know what a transpose was, you'd freak out. Who uses a 2x8 matrix? When am I ever going to see this in real lief? You won't, but it's not important. You won't panic because you know this is an easy problem.

| 1 4 |
| 8 8 |
| 2 9 |
| 4 1 |
| 9 0 |
| 0 0 |
| 2 0 |
| 3 2 |

Easy. Make some up and practice on your own. There's an easy point on your exam.