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Examples : Symmetric and Skew Symmetric Matrices Video Lecture | Mathematics (Maths) Class 12 - JEE
FAQs on Examples : Symmetric and Skew Symmetric Matrices Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is a symmetric matrix? |  |
Ans. A symmetric matrix is a square matrix that is equal to its transpose. This means that for every element A[i][j] in the matrix, it is equal to A[j][i].
| 2. How can we identify a symmetric matrix? | |
Ans. To identify a symmetric matrix, we can compare the elements of the matrix with their corresponding elements in the transposed matrix. If all the elements are equal, then the matrix is symmetric.
| 3. What are some properties of symmetric matrices? | |
Ans. Some properties of symmetric matrices include:
- The diagonal elements of a symmetric matrix are always real numbers.
- The sum of two symmetric matrices is also a symmetric matrix.
- The product of two symmetric matrices is not always symmetric.
| 4. What is a skew symmetric matrix? | |
Ans. A skew symmetric matrix is a square matrix in which the transpose of the matrix is equal to the negation of the matrix itself. This means that for every element A[i][j] in the matrix, it is equal to -A[j][i].
| 5. How can we determine if a matrix is skew symmetric? | |
Ans. To determine if a matrix is skew symmetric, we can compare the elements of the matrix with the negation of their corresponding elements in the transposed matrix. If all the elements are equal, then the matrix is skew symmetric. Additionally, the diagonal elements of a skew symmetric matrix are always zero.
Text Transcript from Video
hello friends this video on matrices
part 32 is brought you by exam fear calm
no more fear from exam before watching
this video please make sure that you
have watched part 1 2 power 31 let's
take one more example we have to express
this matrix as some more symmetric and
skew symmetric middle so here we have to
use the the one that we have so I told
any metal s is nothing but 1 by 2 it
must be - plus 1 by 2 P - P - sorry this
very symmetric and this guy skew Slater
this formula we know I have this a I can
find one by giving us a - that this will
be symmetric matrix and 1 by 2 e - a -
that will be skew symmetric matrix and
that will be answered so let me find
this is a is 3 by 1 minus 1 let me find
a - that will become 3 by 1 minus Rho
times column becomes Cup now I have to
find a symmetric part symmetric part is
nothing but 1 by 2 8 + P - is what 3 by
1 minus 1 plus 1 5 minutes this is
nothing but 1 by 2 into 3 plus 3 is 6 5
plus 1 is 6 1 plus 5 is 6 minus 1 plus
minus 1 is minus 2 so 1 by 2 into this
and that's come out to be 6 by 2 is 3 6
by 2 is 3 6 by 2 is 3 minus 2 by 2 is
minus 1 this is my symmetric bar
similarly skew symmetric 1 is nothing
but 1 by 2 e - a - correct this way
which is nothing but 1 by 2 this matrix
3 by 1 minus 1 minus 3 1 5 miles and
that is nothing but 1 by 2 into 3 minus
3 0 5 minus 1 4 1 minus 5 minus 4 minus
1 minus minus 1 0 and this is nothing
but 0 by 2 0 4 by 2 mu - perfect - to me
so that is my skew symmetric matter so I
can say that this matrix is equal to
this guy Plus this guy where this guy is
symmetric and this guy is skew symmetric
so what I've done I have converted a
matrix as sum of symmetric and skew
symmetric matrix just I've used the
formula this is nothing but 1 by 2 a + a
- plus 1 by 2 a - let us take one more
example this
hey does the same thing you have to
again convert this mate you see do some
of a skew symmetric matrix and symmetric
matrix so if I assume this is a had to
write this as you small 1 by 2 is less
me - no way - E - B - why I am taking
this question is because this is 3 3 by
3 found the last first two by two forms
are just taking it so before doing this
it's fine eight or let's meet right this
way
a mate is nothing but 3 3 minus 1 minus
2 minus T 1 minus 4 minus 1 T I had to
find a - because I have to use a - neow
convert the symmetry column so the
3 3 minus 1 becomes column minus 2 minus
2 1 big pulse column minus 2 minus 2 1
becomes column minus 4 minus 5 minus 2
becomes so this is my a - now I have to
find symmetric part symmetric part is
nothing but 1 by 2 a + a - ok so that is
nothing but 1 by 2 a big common a plus a
- that is really - 18 minus 1 minus 2
minus 2 1 minus 4 minus 5 plus 3 minus 2
minus 4 3 minus 2 minus 5 minus 1 1 this
is nothing but 1 by 2 into so if you saw
this 3 plus C is 6 3 plus minus 2 is e 1
minus 1 plus minus 4 is minus 5 this guy
here minus 2 plus 3 is 1 minus 2 plus
minus 2 is minus 4 1 minus 4 minus 5 is
4 8 minus 4 minus 4 minus plus minus 1
is minus 5 minus 5 plus 1 is minus 4 and
west winds and if you multiply a number
by 2 1 by 2 6 by 2 is 3 correct this
becomes 1 by 2 times minus 5 by 2 1 by
minus 4 by 2 is minus 2 minus 4 by 2 is
minus 2 minus PI by 2 is minus PI by 2
minus PI by 2 is minus 2 and 4 by 2
stream this is my memories so this
symmetric matrix similarly for skew
symmetric SK
that's why I have to find one way to e -
Hey - there's one bite in common same
set 3 3 1 - t - t 1 4 - 5 - is 1 matrix
- 3 - 2 - 4 3 - 2 minus y -1 1 so this
is a and this guy's B - correct this is
nothing but 1 by 2 let's subtract this 3
minus 3 is 0 3 minus minus 2 minus minus
2 is 5 1 minus minus ones 1 sorry this
minus 1 minus 1 minus minus 4 is minus 1
plus 4 is 3 minus 2 minus 3 minus 5
minus 2 minus minus 2 is 0 1 minus minus
5 is 1 plus 5 6 this is minus 4x minus 4
minus minus 1 is minus 3 minus 4 plus 1
minus 5 minus 1 is minus 6 and minus 2
is this is nothing but 0 5 minus 5 by 3
minus 3 by 2 3 and this is my schematics
so I can say that my this guy a is
nothing but sum of matrix Q matrix that
is 3 this guy which I got G matrix 1 by
2 minus PI by 2 1 by 2 minus 2 minus 3
minus Phi by 2 minus 2
this is my skew matrix plus sorry this
is symmetric matrix plus skew symmetry
this guy 0 5 by 2 3 by 2 minus PI by 3 0
3 minus 3 by 2 here so this matrix is
nothing but symmetric matrix plus skew
symmetric so what I have done I have
computed this matrix as sum of symmetric
and skewness why I was able to do
because this was a square matrix since
this was a square matrix I was able to
convert this square matrix B by 3 for me
to symmetry and skew symmetric so thank
you visit exam viacom to watch free
education videos try free online tests
get the best quality study materials
study from the best tutors and mentors
and maximum thanks and sorry
part 32 is brought you by exam fear calm
no more fear from exam before watching
this video please make sure that you
have watched part 1 2 power 31 let's
take one more example we have to express
this matrix as some more symmetric and
skew symmetric middle so here we have to
use the the one that we have so I told
any metal s is nothing but 1 by 2 it
must be - plus 1 by 2 P - P - sorry this
very symmetric and this guy skew Slater
this formula we know I have this a I can
find one by giving us a - that this will
be symmetric matrix and 1 by 2 e - a -
that will be skew symmetric matrix and
that will be answered so let me find
this is a is 3 by 1 minus 1 let me find
a - that will become 3 by 1 minus Rho
times column becomes Cup now I have to
find a symmetric part symmetric part is
nothing but 1 by 2 8 + P - is what 3 by
1 minus 1 plus 1 5 minutes this is
nothing but 1 by 2 into 3 plus 3 is 6 5
plus 1 is 6 1 plus 5 is 6 minus 1 plus
minus 1 is minus 2 so 1 by 2 into this
and that's come out to be 6 by 2 is 3 6
by 2 is 3 6 by 2 is 3 minus 2 by 2 is
minus 1 this is my symmetric bar
similarly skew symmetric 1 is nothing
but 1 by 2 e - a - correct this way
which is nothing but 1 by 2 this matrix
3 by 1 minus 1 minus 3 1 5 miles and
that is nothing but 1 by 2 into 3 minus
3 0 5 minus 1 4 1 minus 5 minus 4 minus
1 minus minus 1 0 and this is nothing
but 0 by 2 0 4 by 2 mu - perfect - to me
so that is my skew symmetric matter so I
can say that this matrix is equal to
this guy Plus this guy where this guy is
symmetric and this guy is skew symmetric
so what I've done I have converted a
matrix as sum of symmetric and skew
symmetric matrix just I've used the
formula this is nothing but 1 by 2 a + a
- plus 1 by 2 a - let us take one more
example this
hey does the same thing you have to
again convert this mate you see do some
of a skew symmetric matrix and symmetric
matrix so if I assume this is a had to
write this as you small 1 by 2 is less
me - no way - E - B - why I am taking
this question is because this is 3 3 by
3 found the last first two by two forms
are just taking it so before doing this
it's fine eight or let's meet right this
way
a mate is nothing but 3 3 minus 1 minus
2 minus T 1 minus 4 minus 1 T I had to
find a - because I have to use a - neow
convert the symmetry column so the
3 3 minus 1 becomes column minus 2 minus
2 1 big pulse column minus 2 minus 2 1
becomes column minus 4 minus 5 minus 2
becomes so this is my a - now I have to
find symmetric part symmetric part is
nothing but 1 by 2 a + a - ok so that is
nothing but 1 by 2 a big common a plus a
- that is really - 18 minus 1 minus 2
minus 2 1 minus 4 minus 5 plus 3 minus 2
minus 4 3 minus 2 minus 5 minus 1 1 this
is nothing but 1 by 2 into so if you saw
this 3 plus C is 6 3 plus minus 2 is e 1
minus 1 plus minus 4 is minus 5 this guy
here minus 2 plus 3 is 1 minus 2 plus
minus 2 is minus 4 1 minus 4 minus 5 is
4 8 minus 4 minus 4 minus plus minus 1
is minus 5 minus 5 plus 1 is minus 4 and
west winds and if you multiply a number
by 2 1 by 2 6 by 2 is 3 correct this
becomes 1 by 2 times minus 5 by 2 1 by
minus 4 by 2 is minus 2 minus 4 by 2 is
minus 2 minus PI by 2 is minus PI by 2
minus PI by 2 is minus 2 and 4 by 2
stream this is my memories so this
symmetric matrix similarly for skew
symmetric SK
that's why I have to find one way to e -
Hey - there's one bite in common same
set 3 3 1 - t - t 1 4 - 5 - is 1 matrix
- 3 - 2 - 4 3 - 2 minus y -1 1 so this
is a and this guy's B - correct this is
nothing but 1 by 2 let's subtract this 3
minus 3 is 0 3 minus minus 2 minus minus
2 is 5 1 minus minus ones 1 sorry this
minus 1 minus 1 minus minus 4 is minus 1
plus 4 is 3 minus 2 minus 3 minus 5
minus 2 minus minus 2 is 0 1 minus minus
5 is 1 plus 5 6 this is minus 4x minus 4
minus minus 1 is minus 3 minus 4 plus 1
minus 5 minus 1 is minus 6 and minus 2
is this is nothing but 0 5 minus 5 by 3
minus 3 by 2 3 and this is my schematics
so I can say that my this guy a is
nothing but sum of matrix Q matrix that
is 3 this guy which I got G matrix 1 by
2 minus PI by 2 1 by 2 minus 2 minus 3
minus Phi by 2 minus 2
this is my skew matrix plus sorry this
is symmetric matrix plus skew symmetry
this guy 0 5 by 2 3 by 2 minus PI by 3 0
3 minus 3 by 2 here so this matrix is
nothing but symmetric matrix plus skew
symmetric so what I have done I have
computed this matrix as sum of symmetric
and skewness why I was able to do
because this was a square matrix since
this was a square matrix I was able to
convert this square matrix B by 3 for me
to symmetry and skew symmetric so thank
you visit exam viacom to watch free
education videos try free online tests
get the best quality study materials
study from the best tutors and mentors
and maximum thanks and sorry
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