Good day students in this clip were going to be going over an easy trick or method for
multiply matrices in the forget to go to mathgotserved.com of to see what collection of great math tutorials.
Right let's take a look at the first example of problem number one is a were to find of
the product of these two matrices two one four five are multiplied by three two five
one okay let's a were to find the product is to matrices of course the product of matrices
are not always defined so for so we have to determine if the product is defined that can
be done by looking at the dimension of a matrices this has to Rosen to: so this is the two by
two oh in neuritis in the bottom so this is a two by two matrix and this matrix right
here the two by two matrix now how do we know if the of product is the find what we do is
we look at the column of the first of the of the called with the call this the multiply
matrix multiplier in then we can call that the multiply can't matrix okay right so we
look at the column of the multiply matrix and the role of the multiply can matrix and
what ask ourselves are these two numbers the same as is number and is number our data same
in the answer is yes so said it equal that we can multiply them okay. The product is
the find what is the dimensions of the product going to be to determine that you look at
the role of the multiply matrix and that on the of column of the multiply can matrix and
that will be the dimensions of our product so we should expect to get it to by two matrix
as the final result right now since is determined that the product of these matrices us to find
of let's go ahead and use of the trick I was going to show you so why is it important why
am I doing this tutorial make sure you this trick well multiply matrices is not that difficult,
but the process can get cluttered okay and when you have quadrant the workspace is very
easy to make little arithmetic errors with Joseph your answer is with the have blanketed
I flex eight on we could start to invert numbers and make us to the mistakes so the definitely
pain that's why of abolishing this method okay so what you going to do is you going
to basically of set up your product in such a way that it's very difficult to make mistakes
always been is basically saying us also for success okay so I'm going to take the multiply
the way that you multiply matrix and angle with that first before I see how to do this
is you multiply the role in in the multiply matrix by the column of of the multiply can
matrix okay you multiply like this and then you do that and then you do this any go to
bottom and that embodiment in this again the cube enrolled has caller times column and
that's how you get your answer. So that rotation back-and-forth between rows and columns the
multiply matrix and the multiply can matrix is a lot of room for mistakes and disorganization
okay so that's why, one issue disclosure it so just remember that you multiply the Rose
of the first to multiply matrix with the column of the multiply can the second matrix okay
now, with that in mind with me show you how to set this up what you do is you take the
Rose and the multiply multiply matrix and my demise coordinates okay this is the time
to buy to so let's write it as a of X to the massacre next to life's is to, for for the
first wrote it to come of four and then for the second row one, five so into dimensions
you can think of this is X Y X Y right now this is the co-part of will going to write
down the columns in the multiplicand matrix in a horizontal orientation right so three
two is the column in in in the second matrix right here. So write it as three, two right
and then five one I'm going to oriented in a horizontal fashion five, one right to is
go over this again to multiply arose that the Rosen the multiply matrix right him just
as is, but the columns in the multiply can matrix the second matrix and multiply by you
just oriented horizontally okay right now that I have a set up like this is such as
this cake of from here on out so what were going to do is basically multiply the numbers
by multiplying I'm corresponding coordinates okay so excess times X Y can't why and you
find the Psalm of the products okay so for this of coordinate and that coordinate doesn't
going to the first entry two times three is six plus four times two eight okay what six
is eight fourteen so that the first entry in our resultant matrix of mining the one
times three three plus four times to ten three percent thirteen right, one and then if two
times five multiply the X is ten plus the wise four times one for added of fourteen
okay and then the next one we have one times five five plus one times five five of them
together get ten so your our final matrix the product of this to matrices is fourteen
fourteen thirteen and ten right so there you have it. let us take a look at another example
just to make sure we have this down problem number two so let's find the product of of
the following matrix two three one five find this times of one two two five and then three
two okay now first of all we going to find the multiply we have to determine is the product
is defined so let's go ahead and determined that real quick this is the two by two matrix
and this has to Rosen three columns to buy three the call the column from row from the
multiplier matrix is equal to the role of the multiplicand matrix to that's excellent
to that means that we can multiply these two matrices right and the resulting answer the
answer for product is going to be to buy three matrix so can keep that in mind so's is a
product is defined let's go ahead and find the product okay now let's set up our of our
grade like we did before we have to rose for the X forty multiply matrix and for multiplicand
matrix we have three columns so that a make it sufficiently large to compensate for that
size right so for multiply matrix with copying the Rose downcast
is why has
coordinates two