The number of symmetric matrices of order 3 t | vedclass

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(D) symmetric matrix $A$ of order $3 	imes 3$ is defined as $A = A^T$. For a $3 	imes 3$ matrix,it takes the form: $A = \begin{bmatrix} a & b & c \

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$10^6$

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(D) symmetric matrix $A$ of order $3 	imes 3$ is defined as $A = A^T$. For a $3 	imes 3$ matrix,it takes the form: $A = \begin{bmatrix} a & b & c \ b & d & e \ c & e & f \end{bmatrix}$ Here,the independent entries are $a, b, c, d, e,$ and $f$. There are $6$ independent positions in the matrix that can be filled. Each of these $6$ positions can be filled by any of the $10$ digits from the set $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$. Therefore,the total number of such symmetric matrices is $10 	imes 10 	imes 10 	imes 10 	imes 10 	imes 10 = 10^6$.

The number of symmetric matrices of order $3 \times 3$,with all the entries from the set $\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$,is:

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