00:00Hi guys, so this is
00:02just a quick introduction to
00:04matrices. So I have a
00:05definition here for you. What
00:06is a matrix? It is
00:07a rectangular array of quantities
00:10or expressions in rows and
00:12columns. So a bit like
00:13this. If you've ever seen
00:15the movie, the matrix, that's
00:16kind of what we're dealing
00:17with. Right? Numbers in rows.
00:19So these are rows three
00:20rows and columns. One, two,
00:23three, four columns. And that's
00:24important. That is the order
00:26of the matrix.
00:28I'm going to go through
00:28a few different things here.
00:30But the order of the
00:30matrix is rows times column.
00:34So an m by n
00:36matrix is the number of
00:38rows times the number of
00:39columns. So this is three
00:40rows and four columns. So
00:42this is a three by
00:44four matrix. This is a
00:47three by one matrix. This
00:49is a one by four
00:50matrix. This is a two
00:51by two. This is a
00:52two by three and this
00:53is a two by two.
00:54So you got to get
00:55the hang of what?
00:56the order of a matrix
00:58is. So look matrices are
01:00used a lot in mathematics
01:02because it's kind of a
01:03very nice neat way to
01:05store information or to store
01:06numbers. So these numbers couldn't
01:10mean something. I'm going to
01:11get to the applications of
01:12matrices. And later in later
01:16lessons in later topics, you'll
01:18see the matrices comes up
01:19in topic one, topic three
01:22and topic four.
01:24Okay, so yeah, the next
01:26thing I want to talk
01:27about was order, which I
01:28kind of haven't talked about
01:29already, then the elements of
01:30a matrix. So often you'll
01:32see a matrix written like
01:33this. So these are referred
01:36to as in this way.
01:38So the elements. So this
01:40is a one one. So
01:41this is the one one
01:43is the first row, first
01:45column. One two, first row,
01:47second column. One three, first
01:49row, third column. One N,
01:51the first row, and
01:52So this would be, so
01:54this number here would be,
01:56if this matrix was called
01:59A, it would be A24.
02:02This would be 3, 4,
02:04this would be 3, 2,
02:05etc. And it goes all
02:07the way down to A,
02:08M, and so these are
02:09the elements of the matrix.
02:12This is a column matrix
02:13or a column vector. This
02:17is a row matrix, so
02:18the column matrix or column
02:20vector
02:20just has one column and
02:24the row matrix just has
02:25one row and obviously this
02:28one has four columns but
02:29it could be I mean
02:30it could have more than
02:31four columns it could have
02:32three two whatever one column
02:35a square matrix is when
02:37m and n are the
02:39same so this is a
02:39two by two the square
02:40matrix you could have a
02:42three by three four before
02:4320 by 20 whatever zero
02:46matrix when all the elements
02:48So zero and the identity
02:50matrix is when all the
02:54numbers on the diagonal are
02:56one and everything else is
02:58zero. Now it doesn't have
02:59to be a two by
03:00two, but it does have
03:01to be a square matrix.
03:02So this is also the
03:03identity matrix 1, 0, 0,
03:070, 1, 0, 0 like
03:11this. That is an identity,
03:14an identity matrix as well.
03:16Okay, so that's just a
03:18very, very quick introduction to
03:21major says. Obviously in the
03:22next lessons we're going to
03:23get into a lot more
03:24detail in how we use
03:28major says and what operations
03:33and various things that we
03:34can do with major says.
03:36So yeah, I'll see you
03:37in those next videos.