Examples : Transpose of matrices Video Lecture | Mathematics (Maths) Class 12 - JEE

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power 27 this is one example where I
told that one property maybe have told a
B - B - B - B - you to verify the same
property using this example mayor a is
equal to this and B is equal to the
student lesser so let us do this who
this is the first thing people do is you
define a B then take transpose and then
you try and find me - a - and then
multiply so let's must find a me a B is
nothing but you multiply 1 minus 3 with
minus 1 so before multiplying let's
check whether bundling is possible or
not 1 2 3 horizontal to 1 vertical is 3
cross 1 1 horizontal 3 vertical 1 cross
2 u 1 + 1 matches that lease yes you can
multiply and the final amount will be 3
cross 3 matrices so let's do the
multiplication normal so this guy will
become 1 into first row first column 1
into minus 1 minus 1 this guy become
must row second cup
why do you third guy first row second
column 1 2 1 1 simply this guy will
becomes the second row first column that
is minus 4 into minus 1 that is for this
they have become minus 4 into 2 he this
we have become minus 4 into 1 minus so
really this guy 3 into minus 1 minus 3
this guy 3 into 2 6 and this guy 3 into
1 so I've got a B now we have to find a
B transpose
just might be a bit transpose what we
can do is we have a B again the murders
rows to columns on this guy we have got
you'll be like in this fashion similarly
for 8-4 and like in this fashion - three
six three already in this fashion so
this is my LHS so RHS we have to take a
transpose of B transpose of B and
multiply so let me get the transfer of
me first
so this is B transpose of B all the rows
into columns get minus one to one
correct this I wrote in this fashion
similarly e - will be nothing but
convert this column to toe this is my a
- Alice's is nothing but B - into E -
that is - 1 - 1 into 1 minus 1 same
thing here also you take it all of this
and column of this of course element
that becomes minus 1 into 1 that this is
minus 1 if you want to check the
feasibility greater than 1 it is
possible or not begin to that one two
three horizontal into one vertical 3
cross 1 1 horizontal 3 vertical this one
and one matches yes you can multiply and
the result will be 3 cross 3 so the
finer the second element will be you
take this first row second column minus
1 into minus 4 is 4 third is minus 1
into this guy that is minus 3 now I'm
going to take the second row first
column 2 into 1 is 2 2 into minus 4 is
minus 8 2 into 3 is 6
certainly 1 into 1 is 1 1 into minus 4
is minus 4 1 in is least so I have got
this you compare these two they are
equal under second this is minus 8 it
has to be minus 8 let's see what wrong
with it here - boring who is minus -
minus 4 into 1 is 4 minus 4 into is
- this is - a if you see both are same
actually all the elements are saying the
order is same both are 3 cross 3 thus we
can say that if we transpose nothing but
we transpose into V transpose very
simple we just found a V transpose would
turn on V transpose a transport and we
equated LHS is equal to RHS let's take
for example we have to verify that a -
into a is equal to I for this particular
scenario where a is a mattress cos alpha
sine alpha minus sine alpha cos alpha so
before doing that the first unit is in
transpose it's finally transpose convert
row 2 column so this is this and take
row and begin to column caused by sine
alpha second row I will make it a column
minus sine alpha and so I've got a -
I've got a let me multiply them and see
what does the deserve a - into a you see
is nothing bad cos alpha minus sign up
I'm writing it as first into sine alpha
cos of this I am going to multiply with
a this guy
so let me write a cos alpha sine alpha
minus sine alpha and cos alpha so I've
got a - this guy in this guy and let me
multiply this so we'll take horizontal
of this and vertical of second time so
you see this is 2 cross 2 and this
fellow so 2 cross 2 so we can check and
can find that your multiplication is
possible because the head of the center
of this matches the final will be 2
cross 2 so let's say the first item that
guy will be you take this row and this
column multiply and
so cause I'll find gossip vice cos
square alpha - I'm trying to -
enterprise plus signs well so this guy
is caused by a popular Sciences second
element for this you pick first joint
second column the one who's fired him
and this is fun
see cause I'm trying to sign up files
and sign on glass - sine alpha cos alpha
is minus sign in front awesome correct
similarly this element is nothing but
you take this guy and multiply with the
first column sine alpha cos alpha plus
cos I'm trying to - anymore - cause then
you have take the second guy and second
guy this sign in Phi 2 sine Phi sine
square alpha plus cos alpha cos alpha is
cos square alpha you see the sine square
alpha plus cos Phi is 1 we know from
geometry plus cos alpha sine alpha minus
sine of a gospel is gone become zero
similarly here also sine alpha cos alpha
minus cos alpha sine qua this also is
zero and sine square alpha plus cos
twice
this is nothing but my identity matrix
and as I drew LHS is meant to RHS
because I started with a transpose into
a and I got that as nothing but I thank
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