Find the inverse matrix using the
Gauss method, here, right now in this
math channel called
Math with Juan.
[Music]
[Music]
How are you guys and girls? Let's go
right now to find the reverse matrix
using the Gauss method and the
matrix that I have prepared to calculate
its inverse is the following -4, 2 less
1, 2, 0, 1 and minus 2, 3, 1. Very good. Well, then
the inverse matrix can be found from
many ways. In the method of gauss lo
that is done is the following: we
we write the matrix
minus 4, 2, minus 1, 2, 0, 1 and minus 2, 3, 1 and their
right we write the unit matrix,
in this case three rows, three
columns, some on the diagonal and of what
it's about manipulating the rows of
convenient way so that after
to do this by a few steps
let's get something like this:
to the left, for after giving these
smart steps, we have to be
capable of expressing this here and of having
here the unit matrix and in this other
side, on the right, a, b, c, d, e, f, g, h, i, in this
the other side because we'll get another matrix and
this will be the one you want
inverse matrix. Well, let's go to
to start taking these smart steps
to turn what we have here into
something similar to this other and this will be the
inverse matrix.
Okay, first step.
The first row I have I'd like
that looks like this, of course it does, and
Here's a 1, so come on, I'm going to
to get,
I'm gonna try to get a 1 here.
And what do you have to do to get a 1,
when I'm a minus four? Guys,
girls if I want a 1 here I'm going to have to
multiply everything by at least a quarter. If
I multiply this row here by
minus a quarter I'm going to get what
next:
minus four for minus a quarter is 1. 2 for
minus a quarter is minus a half and
minus 1 for minus a quarter is a quarter,
a quarter, and here I'll have minus a quarter.
because one for at least a quarter is less
a room, here 0, 0 and here I do nothing of
moment, so I'll have this as it is and
this, too. I don't touch this. Okay, so
we've already taken the first step. Let's go to
for the second and we'll look,..., at our
objective will be to look at the second
row and get a zero, get a zero,
here's a two because I want a zero. And
How can I get a zero? Well, what
let's do is multiply, multiply
it
first row for 2,..., not for 2, for at least 2!
we're going to multiply the first row by
minus 2 and we're going to add it to the
and for that I'm going to erase this,
I don't need it anymore. I don't need it anymore.
I need and in this part of the board I will do
this little operation: I'm going to
multiply all this by at least 2,
I multiply the first row by minus 2.
minus 2, -2 by 1 is minus 2,
-2 by at least one means, that is 1 and minus 2
for a quarter is less than a half. And
I would therefore have less than 2 for less than a quarter
is
one half, one half. Here 0, here 0 and I said
that what's here I'm going to add to the
second row, I mean, I'm going to do the
next sum 0, 1, 0
I do the following sums, guys and
then here would have a zero here would have a 1,
here one minus one half, this is one half,
here I would have a medium too, here
I'd have a 1 and here I'd have a 0. So.
this, this, this, this, this matrix construct is going to
be as follows:
1, one down
a half, a quarter, minus a quarter, 0, 0
and instead of writing this I write the
equivalent, row, equivalent:
0, 1, a half, a half 1, 0. And this there is
here as it is because it is not yet
I've played so as, as it is, it's done.
Well, let's go for the next one.
step and in the next step we are
we'll lock on to the third row. Let's manipulate,
let's manipulate the third row now.
In the third row I'd be interested in having
also here a zero. And how can we
to get a zero here, as we can
to get some zero so that, so that
this look like this? It's very easy,
multiply this row by two and you'll get it.
we add to the third.
[Music]
We say it and we do it, we say it and we do it
we do. Let's see, let's see, let's see, let's see.
[Music]
Front row.
We add it up, we multiply the number 2,
i.e. the first row multiplied
by the number 2 will be
2, 2 by one is 2, 2 by at least one means is
minus 1, 2 for a quarter this is a half.
This will be less a half
0, 0 and here we put the third row: minus 2
3, 1,
0, 1 and add boys, add and then
summing up, I'll have the following: two,
I'll have a 0 here, I'll have a 2 here, here.
I'll have 3 means, 3 means, here I'll have
minus a half, here 0 and here one, very
All right.
This is the line, this is the line I'm going in.
to write substituting this other
and to do it,
and to do that I need to erase
obviously. I don't need this and I continue
here writing our...
our steps, our, our, our
matrix.
All right, let's go.
Here I'd have a minus one half, a
quarter, minus a quarter, zero and zero. Here
I'd have 0, 1, a half, a half again,
1 and 0 and finally this row.
I don't write it anymore, I write this one that
is 0, 2, 3 medium, minus one medium, 0 and 1.
144 00:08:27,740 --> 00:08:34,740 I'm gonna erase, I'm gonna erase things that already
I don't need to. Look what's here.
we already have in our head. I get rid of
and we don't need this either.
Let's go,
Next step, of course! Now
we're very, very, very interested in that
this two get the hell out of there.
Well, for this 2 to go away from us.
there it would be very convenient to multiply
this for at least 2 and add it to this
line, I mean,
the second row we are going to multiply it by
minus 2 and we add it to the third
row.
Let's do it here. Let's multiply the
second row for 2, for minus 2.
we'd have the following:
zero for minus 2 is 0, 1 for minus 2 is less
2, a mean by minus 2 would be minus 1 and
this would also be minus 1, this would be
minus 2 and this would be zero and this there is
here is the same as before
and what we're going to do now is add up
add, add this row multiplied by
minus two with this one. So adding up,
summing up we would obtain the following: three
means minus 1, 3 means minus 1 would be
equal to a half, okay? A half and
minus half minus one, minus one half
minus one would be equal to minus three means
and this would be minus two and this would be one.
So, boys and girls,
this next step, summarized, in
in a nutshell, we're left with the
Here's how:
this would be the first row, this would be the
first row, this would be the second row,
Come on, come on and this would be the third row:
zero, zero, a half,..., is this okay,
Right? Yes, this looks good. A
and this would be minus three means,
minus three means and this would be minus two,
and this would be 1, 1 olive. Okay, it's very
All right.
I'd love this to be a 1, then.
very easy Juan, very easy. I multiply everything
by 2, multiply all by 2. And multiplying
everything for 2 look what happens, look what happens.
All right, then.
In the first row and in the second row
It's okay.
1 - a half, a quarter, minus a quarter,
0, 0 and nothing happens here either. 0, 1, a half,
a half, a half here too, 1, 0. Multiplying
everything for 2 would have 0, 0, 1. All right, I've got something.
relevant!
Multiplying this by 2 would have
minus 3, multiplying this by 2 would have
minus 4 and multiplying this by 2.
I'd have a 2, a 2. All right, all right, all right, all right.
Let's make room, we don't need this anymore.
That's it. That's it. Well, let's see, let's see,
Let's see, let's see.
I'd love it, I'd love it here.
there would be a zero and this is easy to
to get, of course I do. So that here
there'd be a zero the only thing I'd have to.
to do would be to multiply all this by
minus one half
and add it to the second row i.e., the
third row I multiply by at least one
and I add it to the second row.
We're gonna do this, we're gonna do this.
here. Again. The third row is
I multiply by at least a half, that is,
zero,
0, 1 for at least a half. Well, minus one
medium. Minus three for minus a half
would be three ways. Minus four for less.
A half? Well, that would be two and two for less.
A half would be minus one, okay? And I'll add it to that.
the second row. The second row will be
0, 1 a medium and a medium, 1 and 0.
this little operation I'm going to get here.
0, here a 1 and here a 0 -remember that this is
the second row, this is what
we're gonna get here.
Three means plus one means, that is, three
means plus one means this is four
means but this is equal to two and here
I'd have three and here I'd have minus one.
Okay, okay, okay, okay. Well, I'll just stand over here and
we rewrote this little monster
matrix of
the following way, as follows: we have
here one, here less a half, here a
a quarter, here minus a quarter,
here zero and here zero. Here I have zero,
here I have one, here I have a medium, here
I have a medium too.
Ah, eh, he, eh! Careful, careful! I have to write this down,
that I was already sneaking in.
zero, .............................................................................................................................................................................................................................................,
1, 0, of course,
2, 3, 2, 3 minus 1 and finally this:
0, 0, 1, -3, -4 and 2. Now yes, now yes.
and now all that's left for us to do is to be
earrings from the front row. We will
analyze, let's analyze that we have to
do right now to have here a 1 and, ....,
sorry, to have here a 0 and
then to have already finished our
exercise.
Here, as I said before, here as I have
said before, I want a zero and here
I also want another zero. Good.
To obtain here a zero
what I'm going to do is
multiply the second row by, let me see,
by one half, I multiply the second row
and I'll add it to the first one.
Come on, let's do this.
The second row was multiplied by one
I mean, I have zero,
a mean, 0, this multiplied by a
half will be one, this multiplied by one
average will be three means and this
multiplied by one means will be less than one
and I add the
first row. The first row is
one, minus a half, a quarter, minus a
fourth,
0, 0. Well, by doing this little thing.
operation I'm going to get my new first
row.
One, zero,
a room and here I'll have a minus one
A quarter? A quarter to a quarter? Well, this goes
to be equal to three quarters, three quarters.
And three media plus zero. Three means and
I'll have less than a half here. Then, then,
then, then I can write, I can
write
this thing like, well, like this other one:
1, 0, a quarter,
here three-quarters, here three-half, here
minus a half. This as it is: 0, 1, 0. This 2,
3, -1 y 0, 0,
1, -3, -4, 2. That's good, that's good! Let's erase a
a little, let's erase this, like this, like this,
this also like this and let's close here this...
this, this matrix parenthesis. Okay,
then the next step and the last one goes
to be getting rid of this, ha, ha, ha, ha.
We're about to finish, what a thrill.
only separates us
[Music]
to conclude this exercise
to eliminate this that here, we have to
get rid of a room and the best
way to get rid of a room is to
multiply the third row by at least one
and then add it to the first one.
row. Come on let's do this very thing that
I'm saying here.
This row here is multiplied by
minus a quarter and I'll get the following:
0, 0, minus a quarter.
-3 for at least a quarter will be three quarters and
minus four for minus a quarter will be
simply 1 and 2 for at least a quarter is going to
be less
a medium
and this that there is here I add it to the
first row. The first row is 1, it's 0, it's a
fourth, ..., what else, is three quarters, is three
means and is also less a means.
Well, doing this sumita,
making this sumita -I'm going to write
here a little lower the result
because then I'll copy it here. Let's see,
making this sum I will have 1, 0,
this and this is canceled, zero fantastic,
we already have 1, 0, 0, 1, 0, 0. And 3 quarters plus three.
rooms...
Let's see, three quarters plus three.
quarters ... this is 3 and 3 6, 6 quarters equal to
three means. This is 3 means.
So this will be three quarters plus three
rooms is three half and one more
-let's see-, one more -I'm doing this one
operation-, one plus three means this is going to be
equal to 5, 5 half boys, 5 half girls.
Well, means here. And less a
a half minus a half? This is easy. This
is going to be equal to minus 1, -1, -1.
Oh, good! Well, I'll erase what's here, I'll erase
this that there is here and simply, for
finish, I still have to write this row in
your site -which is the first row, is the
first row. I'm going to write the matrix a
a little higher because you see? It's like my
morale was low and I'm going down, I'm going
downgraded. Well, here I would have
1, 0, 0,
here I would have three means, five means and less
one. Here I would have 0, 1, 0, 2,
3, -1 and here I'd have 0, 0,
1, -3, -4 y 2.
Well, it seems to be, it seems to be that we have
arrived at
the desired result. See?
On the right we have the matrix
identity, in this case 3 by 3, in the
diagonal all some, the other zeros and
then this here would be the
inverse matrix.
All right, all right, all right, all right, all right, all right.
All right.
Well, this is over.
All that's left for me to do is write this of a
the prettiest way. Let's do a little
cleaning, let's do a little cleaning and
let's finally write down what we have
obtained. What we have obtained is what
next: we start from a
matrix, of a matrix that was minus 4, 2,
minus 1, 2, 0, 1 and minus 2, 3, 1. We had this one.
matrix and we've come to get your
inverse matrix and its inverse matrix is
this one here:
three means, five means, minus one, what
plus, two, three minus one,
-3,
-4 and 2. Well, that's it,
that's it.
It only remains for me to say that if I
will multiply this matrix by this one.
I would get
the matrix identity, that is, it would obtain
what's in here.
B,ueno then nothing else, nothing else boys and
girls. I say goodbye to you, see you
in another video. Subscribe, come on,
See you soon!
Goodbye, goodbye, goodbye.
[Music]
[Applause]
[Music]
For more infomation >> Receta de 'Eggs rolls' de cerdo y camarones para consentir a Chyno Miranda | Delicioso - Duration: 10:06. 
For more infomation >> Ricardo de la Puterea Dragostei, declarație de dragoste emoționantă pentru Raluca! A făcut totul pub - Duration: 5:32. 
For more infomation >> Alarma: la condición de salud de Massiel es mala, ¿qué le pasa? - Duration: 8:19. 
For more infomation >> Dev Vlog Sauver le Monde 01/02 - Signalement de joueurs, choix de héros et plus ! - Duration: 3:05. 
For more infomation >> Yarol Poupaud parle de ce seul endroit "où on foutait la paix" à Johnny Hallyday - Duration: 1:53. 
For more infomation >> Como Parar de Fumar Urgente - Duration: 4:23. 
For more infomation >> Obsèques de Michel Legrand : l'émotion de sa veuve Macha Méril soutenue par Brigitte Macron - Duration: 1:28. 
For more infomation >> "Ce lapsus graveleux" de Brigitte Macron qui a provoqué "un fou rire" chez son mari - Duration: 1:39. 
For more infomation >> Réalité virtuelle à 360° au Centre de simulation de la Faculté des sciences infirmières - Duration: 4:07. 
For more infomation >> Dieta de Cha Para Emagrecer Rapido - Dieta Chá 45 Dias - Duration: 5:16. 
For more infomation >> BBB19: Ana Clara surge com roupão de líder e faz revelação importante - Duration: 3:15. 
For more infomation >> Receta de 'Pavlova de fresa con dulce de leche y crema batida' | Delicioso - Duration: 7:06. 
For more infomation >> Receita Para Parar de Fumar - Duration: 6:44. 
For more infomation >> Gad Elmaleh se fait virer d'une scène de Montréal - Duration: 1:12. 
Không có nhận xét nào:
Đăng nhận xét