The number of symmetric matrices of order 3 - 3 all of whose elements are either 0 or 1 is

[ a amp; b amp; c; nbsp; b amp; d amp; e; nbsp; c amp; e amp; f ] nbsp; To fix a, b, c, d, e f every element has two options either 0 or 1. So 2 ...

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Standard XI

Mathematics

Symmetric Matrix

The number of...

Question

The number of symmetric matrices of order $3 \times 3$ all of whose elements are either 0 or 1 is

256

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128

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Solution

The correct option is C 64
$⎡ ⎢ ⎣ \begin{matrix} a & b & c b & d & e c & e & f \end{matrix} ⎤ ⎥ ⎦$

To fix $a, b, c, d, e f$ every element has two options either $0$ or $1$ .

So $2^{6} = 64$ ways.

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Similar questions

Let

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The number of symmetric matrices of order 3×3 all of whose elements are either 0 or 1 is

The correct option is C 64⎡⎢⎣abcbdecef⎤⎥⎦ To fix a,b,c,d,ef every element has two options either 0 or 1. So 26=64 ways.

The number of symmetric matrices of order $3 \times 3$ all of whose elements are either 0 or 1 is

The correct option is C 64
$⎡ ⎢ ⎣ \begin{matrix} a & b & c b & d & e c & e & f \end{matrix} ⎤ ⎥ ⎦$

To fix $a, b, c, d, e f$ every element has two options either $0$ or $1$ .

So $2^{6} = 64$ ways.