This content explains the fundamental concept of scalar multiplication of matrices and demonstrates how to perform operations involving scalar multiplication combined with matrix addition and subtraction.
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in this video we're going to focus on a
scalar multiplication of matrices so
so
let's begin with matrix a let's say it's 5
5
negative 2
7 3
and matrix b
we're going to say it's negative 4 6
negative 2 and 9.
now let's find the values of 3a
3a
and 4b
so 3a all we need to do is multiply
matrix a
by three
so every element in this matrix
we're gonna multiply it by three
so three times five is fifteen
three times negative two is negative six
three times seven is twenty-one
3 times 3 is 9. and that's it
so for 4b it's just going to be 4 times
so 4 times negative 4
that's negative 16. four times six is twenty-four
twenty-four
four times negative two is negative
eight four times nine is thirty-six and
and
that's scalar multiplication
now you also need to be familiar with
operations uh associated with matrices
that involve scalar multiplication and
we're going to go over some examples
now let's say if we want to find the
value of 5a
how can we do that so we got to multiply
matrix a
and then there's going to be a
subtraction sign and then we're going to
multiply matrix b
by 6
or negative 6.
if you multiply by 6 the negative sign
will remain here but if you multiply by
negative 6
you could change it and put a plus sign
which i think it's easier
so first let's multiply this matrix by five
five
so five times five is twenty-five
five times negative two is negative ten
times 7 is 35
5 times 3 is 15.
and then let's put a plus sign and
multiply everything in this matrix by
negative 6.
so negative 6 times negative 4 is
positive 24
negative 6 times 6 is
negative 36
negative 6 times negative 2 is 12
and negative 6 times 9 that's going to
so now
all we need to do
is add the two matrices
and this will give us the value of 5a
so let's add the elements in the first
row and in the first column
25 plus 24
that's 49
and then let's add the elements in the
first row second column
negative 10 plus negative 36
is negative 46.
now let's move on to
second row first column
35 plus 12
is 47
and then finally
the second rule second column 15
15
plus negative 54
is negative 39
and so that's it for this problem
now let's try another example let's say
we have
matrix c
and it has the numbers 4
6 negative 2
3 7 8
8
five negative two three
negative seven
so go ahead and perform this operation
find a matrix that corresponds to 3c
and then plus seven
seven
feel free to pause the video if you want
to work on this example
so let's multiply element c i mean
matrix c by three
three times four is twelve three times
six is eighteen
and then three times negative 2 that's
negative 6
and then we're going to have 9 21
21
and 24.
and then let's multiply every element in
matrix d
by 7.
so 7 times 5 is 35
7 times negative 2 that's negative 14.
7 times 3 is 21
7 times negative 7
is negative 49 and then we'll have 28
now let's add
the two matrices
so first let's add 12 and 35
12 plus 35 is 47
and then let's add 18
and negative 14 which will give us 4
and then negative 6 plus 21
and then
we have 9 and negative 49
which is negative 40.
21 plus 28
that's 49
and then 24 plus negative 63
or 24 minus 63
that's going to be negative
negative 39
39
and that's it so now you know how to
perform operations with matrices
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