This content introduces the fundamental concept of matrices as rectangular arrays of elements, explaining their structure, dimensions, and how to identify individual entries.
Mind Map
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so today we're going to be learning about
about matrices
and a matrix is the singular form of matrices
matrices
it just means one matrix but if you're
talking about
matrices you're probably talking about
two or more since it's plural
now a matrix is simply going to be a rectangular
rectangular
array a rectangular array
of elements a rectangular array
now what this means is you're going to
have a box
it's going to have brackets sometimes it
has parentheses but this one is going to
have brackets
and this matrix is going to have two
rows and two columns
the first row is going to be seven eight nine
nine
and the second row is going to be one two
two
three so given this matrix
we know that it has two rows two rows
but we also know that it has three columns
columns
so what i'm going to do is i'm going to
change my color to red and i'm going to circle
circle
all the rows i'm going to circle all the rows
rows
so this is going to be the first row
this 7
8 and 9 and then the second row
is going to be one two three
so rows are always going to go from left
to right
they're always going to go from left to
right so they
are horizontal in a sense
now i'm going to change my color to blue
and i'm going to circle
all the columns so this is going to be
the first column
7 1 this is going to be the second column
column
8 2 and this is going to be
the third column 9 3
so columns are always going to go from up
up
to down so these are going to be
vertical okay
now that's the difference between rows
and columns
and what we do is we can specify a dimension
dimension
so a dimension let me put my color back
in white
what we're going to be doing is we're
going to be defining the dimension of a matrix
all right now this is going to be two
numbers you're going to have a row number
number
times a column number and r just means
how many rows you have
and c is going to be the number of columns
so here our matrix has two rows
and then since it has three columns the
c number is going to be a three
so this is a two by three matrix we say
it has two rows and three columns
and then the last thing we can do is we
can specify
the entry that we're looking at so let's
say i want to specify
this number eight right here well
what i would have to do is first i would
have to give this matrix a name
let's say it's matrix m and that's a
capital m by the way
what we would do is we would write a lowercase
lowercase
m standing for an entry of matrix
m and then we would have to specify the
row number and the column number
so this eight is in the first row
so the row number is going to be one but
it's also in the second column right
so the column number is going to be 2.
so m12 is going to be equal to
8. so if you know the row number
and you know the column number you can
specify any
element in this matrix and the elements
are just going to be the numbers
inside the matrix so that's matrix
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