Symmetric matrix mein diagonal ke upar wale elements aur diagonal ke niche wale elements mirror image hote hain. Isliye, humein sirf 6 positions ko fill karne ki zaroorat hoti hai:
3 diagonal entries:(a11,a22,a33)
3 upper triangle entries:(a12,a13,a23)
Chunaki entries {0,1,2,3,…,9} ke set se li gayi hain, toh har ek position ke liye 10 choices hain.
Total symmetric matrices:
No. of symmetric matrices=106
Explanation
Symmetric Matrix ki Definition
Agar A ek symmetric matrix hai, toh uska condition aij=aji hota hai.
Symmetric matrix mein diagonal ke upar wale elements aur diagonal ke niche wale elements mirror image hote hain. Isliye, humein sirf 6 positions ko fill karne ki zaroorat hoti hai:
3 diagonal entries:(a11,a22,a33)
3 upper triangle entries:(a12,a13,a23)
Chunaki entries {0,1,2,3,…,9} ke set se li gayi hain, toh har ek position ke liye 10 choices hain.
Total symmetric matrices:
No. of symmetric matrices=106
JEE
Let $\left[\begin{array}{cc}\frac{\sqrt{3}}{2} & \frac…
