L35 : Inverse using matrices operation - Matrices, Maths, Class 12 Video Lecture

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watching this video please make sure
that you have watched part 1 - Part 3
for now let's understand a way to find
in verse 4 matrix by elementary
operations they told example you have a
matrix let us suppose 5 6 7 8 or
something you know find the inverse you
say this that this matrix is a leads a
person is some matrix and this into a
inverse is nothing but I 1 0 0 1 so
using my operations row operation for
completion if I can just make this as 1
0 0 1 so this will be 1 0 0 0 1 into a
inverse is nothing but some value I will
get let's suppose any any value lvl this
book ABCD now so this becomes that is I
can say that a inverse ability that it's
very easy to find inverse using
elementary row operation let's still 6
an example actually so we are told that
a is equal to 1 to 2 minus 1 and we have
to find the inverse of this we can do
using both row operation and column
operation let us try to go using your
and solve this bureau operation only
I'll use only rows in the next slide I
will use all the same question in column
operation so using row operation so I
have just this my hello 1 and this is my
Road now let say that a into a inverse
is equal to PI correct so I can write
the same thing as 1 in to minus 1
until 8 inverse is nothing but I so this
is math I can be dimensions this one
this is my eye so now let me do one
thing let me perform the row operation
almost the first thing I have to make
this else 1 1 0 0 this the target is to
make this as 1 1 0 0 as I told if I make
this Foreman 0 0 then that is into 8 vs
some value to find us
so this is already 1 31 so my purpose is
solved
second thing is since this is r1 this is
r2 what I into is I can try to make this
guy as 0 because my final target is 1 0
0 1 correct this has to be this one this
is already 1 this guy is to have to make
it safe so what can I do how can I make
it 0 if I can say that this guy is
nothing but that is r2 is nothing but 2
times R 1 so this becomes 2 minus 21
this becomes L that is the target I have
now see you want to make it 0 or you can
use column operation I have to say C 1
is nothing but C 1 plus 2 C 2 so 2 plus
2 becomes a but I am using a row
operation also I can use these rows only
these nozomi alright so I'll say R 2 is
nothing but R 2 minus 2 1 why because I
wanted to make this guy is if this my
target so this becomes R 1 is unchanged
R 2 becomes R 2 minus 12 that is 2 minus
2 into 0 minus 1 minus 2 into 2 that is
minus 1 minus 4 that is minus 5 but
minus 1 minus x of that is minus 1 minus
4 minus 5 u minus 2 times a 1
in Reverse so a since I performing this
site that you put on the side also our
one remains unchanged our two will
change this becomes 0 minus 2 into 1
that is minus 2 this becomes 1 minus 2
into 0 this is done now the second step
this guy has to be 1 correct so to get
this guy has to be 1 what I can do is I
can multiply our two with minus 1 by 5
this becomes 1 that is one possibility
because if I now subtract this day with
this we have already done now this guy
will get changed I don't want to impact
this I want to affect only this way they
multiply this with some number this guy
zero this won't get changed so I can use
a multiplication so I can say R 2 is
equal to minus 1 by 1 please understand
why I am doing this a little too
difficult for you so R 1 is same this
becomes 0 by 1 by L is 0 minus Phi I
minus 1 by 5 is become into a inverse
becomes Rho 1 is unchanged minus 2 into
minus 1 by 5 is 2 by 5 and 1 into minus
1 by 5 that is minus so I have got these
numbers these number of self change now
my target is this way now if I multiply
this guy this because I'm see them you
know only now a multiply over PI to this
because 1 by 2 so I can multiply not
just apply so I subtract this guy with
this guy I get 1 this day with this way
with 1 St there so I can use subtraction
that means I can say R 1 is nothing but
R 1 - well if I do this fashion sorry I
will make it 0 so I have to say you are
because this minus 2 into R 2 I have to
make it 0 so if I do this this is still
same this slightly change
so what I get is
let's suppose our two is same carbon
becomes alumni Stewart no 1 becomes 1
minus 2 into 0 is again one who becomes
2 minus 2 into 1 that is 2 minus Q zero
Degree inverse becomes this very means
same these guys will change this guy is
our 1 minus 2 R T that is 1 minus T by 4
by 5 there is 1 minus 4 by 5 that is one
better simile this guy becomes 0 minus
minus 2 n minus 1 5 so that becomes 2 by
5 that means what I get is a inverse is
nothing but 1 by Phi T by Phi Phi and
that is nice so what I have done here I
wrote in this fashion into a inverse
equal to I into 8 verses 30 I now my
goal was to convert this guy into this
fashion 1 1 0 0 this this one identity
matrix one was there so I didn't change
it this way I want to make it 0 since I
am using row operation I am by the
multiplying operation month option to
multiply with this some number or add or
subtract another it multiply this with 0
multiplying with 0 is not possible
because multiplication TV is everything
holds four nonzero numbers so I can the
max I can do is I can subtract this
gravid twice of this so that this guy
becomes 0 and that's what I have done
then I got this 0 but this guy's - why
not I want to make it 1 since it is
minus 5 I get whether you can use this
formula multiplication comment to make
it 1 this guy we gave 1 this we have
this guy is - now I have to make it 0
norm I can use the motivation homework
because I can multiply by 0 so I use
this are 2 is square to order - 2 are 2
because 2 minus twice of this becomes 0
and this is not impacted and as I guide
us let's solve the same quotient using
column magnets so I have
is equal to one to two miles at the fine
universe I know a into a verse nothing
but I can use this formula one team same
formula in contain yours is equal to I I
is this or to astrometrics now my goal
here is to convert this guy into
identity form and now I am using only
column operation column operations if
you see one good one is there the first
the second thing I can change is this
guy or this guy but I don't know how to
change this guy if I want to change this
guy using column operation c1 c2 I don't
think it is possible because if I were
going to make it zero I can't use the
zero thing might give zero if I say C 1
is equal to C 1 plus 2 C 2 this becomes
0 but this becomes 1 plus 4 will be
before the film spy I don't want to
change this why can't change this then
you can try changing this so let me try
changing this to change this I have to
make it 0 this becomes nice if I say C 2
is C 2 minus 2 C 1 so this becomes 2
minus 2 0 this works change but this guy
is not in fine you see this guy is not
in fact this guys in fact so what I can
say is C 2 is nothing but C 2 minus 2 C
so what I get here is C 1 is insane C 2
is C 2 minus 2 C 1 2 minus 21 this is 2
minus T 0 minus 1 minus 2 into 2 is
minus 1 minus 4 is minus 1 into a
inverse is equal to C 2 minus 2 C 1 C 1
assistants
C 2 is equal to C 2 minus 2 C 1 0 minus
C into 1 minus T and this becomes 1
minus V 2 0 that is cannot yeah so I
have got 1 0 now my goal has to be this
to make this as 1 this is very simple
because if I multiply this guy the whole
thing by minus 1 by 5 this thing this
will be 0 in this thing with Adama it's
correct so I do that
so AC 2 is equal to minus 1 like so so C
1 is same this becomes 0 2 minus f of X
0 and minus 5 in the minds of my friend
that is 1 in inverse Isabel - this guy
is same and this becomes minus 2 into
minus 1 by 2 by 5 and 1 into minus 1 by
5 is minus right now this is done now
the challenge is this guy I have to make
this zero making 0 is not difficult like
I can say C 1 is nothing but Sigma minus
2 C do one still remains same who
becomes zero away so I can say that C 1
is nothing but C 1 is nothing but C 1
minus 2 C this becomes 1 minus 2 0 is 1
minus 0 is 1 2 minus 2 into 1 this is 2
minus 2 0 just same anymore so this guy
will be mix same margining this this
they have a change this becomes 1 minus
2 nu q fi na minus 4 by 5 correct 1
minus 2 nu into this becomes 1 by 5 and
this becomes 0 minus email to -
wonderful - - gasps in plus 2 by 5 this
is my
so so I say a inversions nothing but 1
by I 3 by 5 to 5 and then very simple so
I can use either of all column you get a
inverse please know what the hand in
case after applying one or more
elementary operations if you obtain all
zeros in one or more two rows then a
inverse doesn't exist
so you keep applying these operations
you get all zeros here or all zeros here
in any row a column you get all 0 that
means inverse doesn't exist thank you
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