Examples : Multiplication of matrices : Part 2 Video Lecture | Mathematics (Maths) Class 12 - JEE

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this example involve conscience also so
who should see if there's a affects so
what do you think what should be the
approach to solve this question okay
which i think is if you can find the
value of left hand side by taking FX and
FY and multiplying them and then try to
see if that is equal to the right hand
side that generally the general approach
which is following most of the questions
so you what we'll do we'll take effects
will take FY because FY is nothing but
you replace power next with value that
far right if X plus y is nothing but you
place X with X plus 5 equals x plus 5 so
what we can do is begin since the LHS is
not simple is complex this defection
wave why they try to simplify and then
it see you press them to is equal to are
just not would've I do something else
but the first thing is we should try to
simplify the LHS so what is FX this con
sex - yes 0 minus cos øx what is f by
same thing is y cos Phi minus sine Y is
sine Y cos Y so this is my FX and if is
a cost way to check if multiplication is
possible this guy is 3 cross 3 3000 to
three particles this guy so three
percent of three particles
but tail of the skater this matches yes
multiplication possible the final output
will be 3 cross 3 fan God will be of
this form C 1 C 2 C 3 C 3 cos 3 matrix
so I will see that f of X into vector
Phi between what if you have 9 values
for a 3 degree so the first will be you
take this value first row and first
column you multiply this and get Nancy
so this guy will become cos x cos y plus
minus 9y sorry plus 0 0 invisible mostly
must element that second element is this
guy first row second column become cos x
into minus sign this
it becomes plus X minus sine cos cos x
minus sin Phi minus sine X cos 1 plus 0
into 0 I can ignore the thought will be
first toid the last column 0 0 1 this
one that will become cos x into 0 0 plus
minus is equal 0 0 0 into 1 0 the second
will be this will be C 2 1 see this very
second row x first column so that will
be sine X into cos Phi plus cos x in
you're saying swine x plus y plus cos x
sine plus 0 is you can also give title
so this this guy will be see to do
second of this and second of this again
wrote second comments so the sine X into
minus 9y snowy next video - fine line
and then cos X into cos 1 and then 0 it
is 0 so plus Z this guy will be second
element of this and last segment of the
second column of this and second row of
this first is 0 hence then we take
column so second drop this and third
column of the the set F by said so this
is sine X equal 0 0 plus Cossacks into 0
0 and 0 into 1 and 0 for third we take
third
you know of this and first common
DG 1 0 into cos y 0 0 into sine by 0 + 1
into 0 0 now what this will mean is C 3
- it is third row second column then
become 0 into sine y 0 0 into cos y 0 +
0 the last will be you take the last row
and the last column and 0 0 0 0 1 2 1 1
cos x cos y minus sine X language what
cos x + y we know that cos x plus y
minus minus r inverse process is fine
here cos x minus sine x minus cos phi
into silence this is nothing but - oh Sh
- this one you guys - plus y is nothing
but sine X cos Phi plus cos of sine
values and this is - - so both are - so
do you take - for me this becomes minus
Phi this becomes zero sine X cos Phi
plus cos x men by the means - this way
this is sine x + y this guy's minus sine
X sine Phi plus cos x possible it is cos
x cos Phi minus when explained me that
is cos x + 1 this is 0 this is 0 this is
0 and this you don't remember what is
cos x + y what is sine x + y then you
can wash mine on trigonometry there are
given a memory tip on how to live on bed
rest
I told Cossacks cost this boss and boss
wants to do things alone so cos x + y
becomes cos x cos Phi minus sign is fan
away that is cos boss - son son Tomas do
things with boss always so sine x + y is
a sine X cos Phi plus cos x minor
I mean I'm gonna explaining this here
because you need you to take some 20
minutes to explain this if you want to
remember cause X plus 9 minus minus plus
angle all this formula easier you can
wash my trigonometry video I think for
class 10 or those and you will get
clearer picture and you can remember
this formula is I've given a very very
good memory to that now going back to
the same problem this if you see there's
nothing but my oh oh you you see f of X
plus y is nothing but this f of X plus y
cos x plus y cos alpha square minus sine
X will become minus sine X plus 1 this
minus this goes by 0 will be 0 sine s
will be sine X plus point this minus cos
Phi cos x will become cos x plus y and
this is cos x + 1 0 is 0 0 0 0 0 and 1
so if you see you compare these two this
is nothing but f of X plus 1 and that is
what we were supposed to and have
sleepovers so what we have done we have
simplified the LHS you use the
trigonometric formula and God else is
then we take one more example we have to
show that the Alexis is not equal to
Allah says we have multiplying two
matrices let's suppose D this is B this
is nothing but B so we prove that a
cross B is not equal to B trusting for
this particular example so let's do this
let's find the LHS Allah this is nothing
but e cross B this is 5 minus 1 6 7 to 1
the first thing we have to check whether
multiplication is possible this guy is
to trust you this guy is also to cross
to wasn't to what he does so if you see
detain of the state of the smash is
multiplication possible what is the
final output that will be 2 cross 2 only
that means that to be something on this
form C
c1 c2 1 z DD correct so this guy is
nothing but the first elements even then
you take the row of this column on this
row of this and commas so you add this 5
into P plus minus 180 T the second
element is c1 to first books you can
come that is by K T 1 yes minus 1
this guy is c2 1 there is a second row
first column is plus 7 this guy is C 2
the second row second column there is 16
1 plus 7 so what you get here is 7 minus
3 so it 10 minus 3 is 7 and just becomes
20 plus 21 that is 33
this guy is 5 minus 4 is 1
this guy is 6 plus 28 is 30 so this guy
is my answer
this guy is my images let's solve our a
system that is Q 1 P 4
enjoy 5-1 see here also we have to check
whether multiplication as possible or
not sometimes it is not possible
so let's shake that sorry do you do
horizontal to vertical surface also you
may do the tail of this head of this
match yes matches so it is possible to
multiply so what is the final output Nam
it will be 2 cross 2 because the head of
this in tail of this is 2 cross 2 so you
will have this kind of format only so
let's get the value C 1 1 row of this
column of this first row first column so
that becomes identified last one induces
the second one is c12 the first row
second power to mean to minus 1 plus 1
is 7 this guy second row first column 25
plus business and this guy chain 2 minus
1 4 into 7 so what you get here is 10
plus 6 16 minus 2 plus 7 by 15 plus 24
that is 39 minus T plus 28 that is
really this is minus so you see this
strain is like this guy is not equal to
describe what the guys are not seeing it
is 7 monthly 33 34 this is 16 539 so I
can say that HS and that is whatever 16
and spoon so the very simple question
just simplified the LHIN simplify
colleges and we compare before that they
are not equal thank you visit exam fair
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