Definition & Concepts (Part - 1) - Determinants, Math, Class 12 Video Lecture

hello friends this video on determinants
part 1 has got you by exam Viacom no
more free from exam what we will study
we will study determinants introduction
we will study determinant of order 1 2 &
3 will study some properties of
determinants will study how to find
areas of triangle using determinants we
study new term called miners and
cofactors link to determinants will
study how to find adjoin and inverse of
a matrix and will also study
applications of determinants and metro
system real-life so before you even
study determinants let's try to
understand why do we need determinants
the same question what will happen if we
don't serve determinants what is that
link we shall miss the line if you study
determinants or where will you use
determinants in your real life maybe
today or in future the first field where
we generally use determinants and very
widely used remains in the field of
science the applying to be in the field
of science in future you want to be a
scientist or engineer in that case
determinant is a master module we use
determinants in free love science also
in the field of computers as I told
matrices are also used in the field of
computer science
similarly determinants are also used in
the field of computer science matrices
are determinants are almost I cut the
same but I guess a determinant is
extension of matrices because we find
determinant of a matrix so if we know
matrix if you know what is metrics then
only we should study determinants so
this matrix is using the field of
computer science to represent data and
then manipulate data
similarly determinant is also used in
the field of computer science
determinant is used you find if three
points if you see in a plane are
collinear not they are they lie in the
same point
they are indifferent their Carini and
non-korean all those things which we can
find using determinant also there is a
Madras we can tell using determinant if
for this particular mattress inverse
will exist or not so inverse of matrix
exists or not you can tell using
determinant if you want to find area of
triangle you know all the coordinates
you know the coordinates this guy you
know the coordinates of this point this
point or this point ABC if you know the
coordinates you can very easily find
area of the triangle using
also if you have two equations for
example T 1 X plus begin violence into C
1 a 2 X plus B 2 y is be receding we can
solve this using determinant normally
also we can solve we know various
methods we have learned in the previous
classes how to solve these kind of
equation but we can also solve using
determinant so going by the application
of ritterman we see that determinants
are widely used in think of science
computers maths engineering horn
officials so that is the reason why we
will study to determine the next life
I'll start you I'll introduce you what
it is determinant was the first
prerequisite for determining this matrix
so if you know met this is good we can
continue with this chakra if you don't
know matrices please pause go to my
matrices video watch the video
understand them in matrices properly
then only come to this chapter because
before understanding what does it
eliminate why do we need neutral main
matrices understanding is must you
should know what is matrices and it
should be comfortable in witnesses once
you are comfortable in matrices then
only you can understand determinant so
what are determinant determinant is
nothing but for every square matrix
please note the first thing is
determinant is applicable only for
square we can associate a number that is
real or complex
and that number is gone dating me
because what happens is CJ Lee the
matrix which we have this form a1 b1 a2
b2 this kind of form and there is no
real number that represents us is very
sometimes cumbersome to not represent
this in this fashion because it is just
nothing but Erik array of numbers this
is two by two Erik so what we do you
represent this guy as a number a real a
complex number and that number is
counted Lebanon so but we will tell you
how to find you terminate for one
transfer matrix 2 cross 2 3 cross 3 and
cross 3 will tell you how to find that
but just know then it remains nothing
but a mapping of the matrices with a
real number this is a real number real
or complex number any number actually so
real or complex number and this side we
have matrices so this mapping this
mapping so this guy's nothing but
determinant so the real and complex
number which is used to represent
matrices called determinant we have wide
application of determinants as I told it
is used to find the area of triangle and
sometimes to find the inverse of the
matrices and that is the reason we are
studying determinants but logically
determine is nothing but for a matrix
will represent that metal is you know as
a real number or being associated matrix
as a real a complex number and that is
called determinant for example if we
have this matrix a b c d this is my
matrix then determinant of this a is
represented by debt a if this is my
address Det e this is how i represent a
determinant and this is nothing but a
with a double bar please note this guy
is not a modulus this is a determinant
determinant of a is nothing but e and
this bars this is the symbol of
determinant of a
and the what is the value of this that
will learn in the next slides but just
understand the naming convention when I
make this a this is the matrix when I
say determinant a I represent that guy
as de ta or a with two bars so matrice
is represent in this fashion if you see
right and mate determinant is this
fashion so please don't get confused
this is generally used for matrix so
when I say here it has it has dumped
ABCD and this guy when I say like this
there is no cut hair this is one day to
a million correct so matrix and
determinant there's a difference so
determined is nothing but an association
of the matrix to a real or complex
number we will tell you how to associate
that and mathematically to represent
that you say de te for determinant of a
and mathematically it is a with two
lines
please note which I already told once
again a is read as determinant of a knot
modulus of the sample when you say X and
X modulus is this we have learnt the
modulus symbol and the determinant
symbol looks almost same but they are
not seen when I say matrix for this
matrix like this this I am saying I am
talking about determinant of a for a
number when I use this I generally say
modulus of a number but for matrix when
I use this two lines that becomes
determinant of the matrix but for a
number when I use this two line that
becomes modulus of the metalic so there
is a difference for number if I use this
two lines
this becomes modulus for example minus
three modulus for matrix if I have a
matrix a matrix a
I use this line that is nothing but
determinant please make a concept clear
here because the only confused between
modulus and imminent
so this guy's always determinant if he
is a mattress it is a number that means
it is a modulus but here in our chapter
we are totally concerned about matrices
and determinants also she will not even
use this term modulus just to avoid
confusion and the second thing has to or
it is for every square matrix you have a
determinant that means only square
matrices can have little name please
note only square matrix can have it mean
you have determinate the first and the
critical condition is that the matrices
has to be a square matrix so now the
question comes how you got this word
aluminum from where you got this word
root minute so there is story behind
this and the story is if you see this
equation this equation you must be
familiar with their two equation linear
equation with X & Y variable a 1 X plus
B 1 y is going to C 1 a 2 X plus B 2 y
is going to C 2
now for this equation we know that if
you want to find whether solution exists
or not how to find that define with this
guy a 1 by a 2 if this is equal to B 1
by B 2 I think you have infinite
solutions and if even by 8 infinite or 0
infinite or 0 if even by a 2 is not
equal to B 1 by B 2 then you have
distinct solution correct same thing I'm
adding here the solution of this
equation whether it has unique solution
or not for this equations for the whole
system of equation whether it has unique
solution or not is determined by a 1 B 2
that is a 1 B 2 minus B doing sorry a 1
B 2 minus B 1 into correct so
this is the guy that determines is known
this is the guy a 1 B 2 minus a 2 B 1 is
the guy that determines whether this
system of equation has a unique solution
or not so a 1 B 2 minus a 2 B 1 please
notice the key here this guy is
determining so this guy is nothing but
determinant for this mission so you see
here the same thing misery wrote here
even V 2 is equal is not equal to B 1 B
2 a 2 by sorry a 1 by B 1 is not equal
to a 2 by V 2
yeah it will a video and here here even
by B 1 is equal to e 2 by B 2 same thing
at least all the same same only so you
see if a 1 B 2 minus a 2 B 1 is not
equal to 0 then the system has a unique
solution and this is what does determine
so for this if I say I have a matrix a
which has this value this is a matrix a
even B 1 a 2 B 2 for this matrix
determinant will be nothing but even we
do multiply this minor e to D so if you
see this guy is nothing but determinant
why because this guy determines whether
this equation has unique solution and
that is why the water dominant has come
just a knowledge for you that the word
determinant has come why because if you
represent this equation this is no
equation in the form of matrix that this
will come this matrix into X Y matrix is
you go to this constant and this is also
matrix so in this equation this this
whole system this whole system when you
want to see whether this system has
unique solution or not this is
determined by determinant this guy is
determined by this
I correct see for this equation we know
that if even B 2 minus a 2 B 1 is equal
to 0 then that is correct so here the
thing that determines where this
equation has unique or non any solution
is a 1 B 2 minus a 2 B 1 the same
equation is representing the matrix form
this is a normal form this is matrix
form this is matrix form so now to see
whether this system has unique solution
or not we use determinants to determine
and this determinant is nothing but even
V 2 minus a 2 V 1 so we will learn will
take more slides where we'll tell you
how to find you terminated for 1 Cross 1
2 cross 2 3 cross V kind of matrices but
this understand the reason why it came
is because determinant is something that
tells you whether the system of equation
has unique solution or not and that is
why the word determinant came now
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