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

Question

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 (A) 12 (B) 6 (C) 9 (D) 3

Tardigrade Admin · Accepted Answer

If two zero's are the entries in the diagonal, then 3 C 2 × 3 C 1 If all the entries in the principle diagonal is 1 , then 3 C 1 ⇒ Total matrix =12

Q. Let $A$ be the set of all $3 \times 3$ 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

12

6

9

3

If two zero's are the entries in the diagonal, then
$^{3} C_{2} \times^{3} C_{1}$
If all the entries in the principle diagonal is 1 , then
$^{3} C_{1}$
$\Rightarrow$ Total matrix $= 12$

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

12

6

9

3

If two zero's are the entries in the diagonal, then 3C2​×3C1​ If all the entries in the principle diagonal is 1 , then 3C1​ ⇒ Total matrix =12

Q. Let $A$ be the set of all $3 \times 3$ 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

If two zero's are the entries in the diagonal, then
$^{3} C_{2} \times^{3} C_{1}$
If all the entries in the principle diagonal is 1 , then
$^{3} C_{1}$
$\Rightarrow$ Total matrix $= 12$