ShmoopTube
Where Monty Python meets your 10th grade teacher.
Search Thousands of Shmoop Videos
Algebra II Videos 54 videos
Mosquitos need their caffeine, just like the rest of us. Wouldn't think zipping around and stinging people all day long sap your energy?
Identity Matrices 870 Views
Share It!
Description:
Identity matrices sound more organized than identity crises, at least.
Transcript
- 00:04
Identity Matrices, a la Shmoop.
- 00:07
Jason Borneo can’t remember anything important about his life… [Man with a bandage on his head]
- 00:10
…his name, his address, his iTunes password… nothing. [Man holds up a name badge with a qeustion mark on it]
- 00:14
All he has in his possession is a briefcase containing a matrix. [Man opens a briefcase that has a note in it]
- 00:18
And a banana, but he’s saving that for later. [Banana appears in the briefcase]
Full Transcript
- 00:21
To learn his identity, Jason must create an identity matrix that corresponds to the matrix
- 00:26
in his briefcase…
- 00:27
…and multiply them together.
- 00:29
The original matrix is 2 rows by 3 columns, with values 2, 9, 34, -90, 32, 1.
- 00:36
An identity matrix is a square matrix whose diagonal is composed of ones.
- 00:40
The remaining values of the matrix are zeroes.
- 00:44
In order to find the dimensions of the identity matrix that correspond to the original matrix… [Matrix written out next to a matrix with a question mark]
- 00:49
…Jason just has to look at the number of columns of the original matrix.
- 00:53
For his 2 by 3 matrix, the corresponding identity matrix would be 3 by 3.
- 00:58
Now he can multiply the two using the standard procedure of matrices multiplication:
- 01:03
2 times 1, plus 9 times 0, plus 34 times 0 is 2…
- 01:08
…2 times 0, plus 9 times 1, plus 34 times 0 is 9… [Arm pointing to the numbers which are being multiplied]
- 01:13
…2 times 0, plus 9 times 0, plus 34 times 1 is 34… and so on with the second row.
- 01:33
The end result when multiplying by any identity matrix is always the original matrix.
- 01:38
We can think of an identity matrix as the matrix equivalent of “1.” [The original matrix next to the identity matrix]
- 01:44
Upon completion of Jason’s mission… [Man with a bandage on his head with his thumbs up]
- 01:45
…a second, smaller briefcase unlocks, containing all of his personal information. [A smaller briefcase inside the original briefcase with a pile of documents]
- 01:51
It turns out he’s a stockbroker living in Pittsburgh. [The man looks surpised]
- 01:53
Hm.
- 01:54
Kind of anti-climactic. [Man looks upset and cries]
Related Videos
Mosquitos need their caffeine, just like the rest of us. Wouldn't think zipping around and stinging people all day long sap your energy?