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Byju's Answer
Standard XI
Mathematics
Symmetric Matrix
The number of...
Question
The number of symmetric matrices of order
3
×
3
all of whose elements are either 0 or 1 is
A
256
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B
128
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C
64
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D
32
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Solution
The correct option is
C
64
⎡
⎢
⎣
a
b
c
b
d
e
c
e
f
⎤
⎥
⎦
To fix
a
,
b
,
c
,
d
,
e
f
every element has two options either
0
or
1
.
So
2
6
=
64
ways.
Suggest Corrections
10
Similar questions
Q.
Let
A
be the set of all
3
×
3
symmetric matrices all of whose entries are either
0
or
1
. Five of these entries are
1
and four of them are
0
.
The number of matrices in
A
is
Q.
Let
A
be the set of all
3
×
3
symmetric matrices all whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.
The number of matrices in
A
such that
|
A
|
=
0
, is
Q.
Let
A
be the set of all
3
×
3
symmetric matrices all of whose entries are either
0
or
1
. If five of these entries are
1
and four of them are
0
, then the
number of matrices in
A
is
Q.
Let
A
be the set of all 3
×
3 skew-symmetric matrices whose entries are either
−
1
,
0
, or
1
. If there are exactly three
0
s, three
1
s, and three
(
−
1
)
s, then the number of such matrices is
Q.
Matrices of order
3
×
3
are formed using the elements of set
A
=
{
−
3
,
−
2
,
−
1
,
0
,
1
,
2
,
3
}
.
Then the probability that matrices are either symmetric or skew-symmetric, is
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