Solution
Step 1: m aur n ki value nikalna
Hame do linear equations di gayi hain:
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4m+n=22⟹n=22−4m
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17m+4n=93
n ki value dusri equation mein rakhne par:
Ab n ki value nikalte hain:
Toh, matrix ka order m=5 hai aur n=2 hai.
Determinant ∣A∣=m−n=5−2=3.
Step 2: Determinant expression ko simplify karna
Hame diya gaya hai: det(n adj (adj (mA)))
Determinant ki properties ka upyog karte hue:
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∣kX∣=km∣X∣ (jahan m matrix ka order hai)
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∣adj(X)∣=∣X∣m−1
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∣adj(adj(X))∣=∣X∣(m−1)2
Yahan X=mA, toh ∣X∣=∣mA∣=mm∣A∣=55×3.
Ab expression ko solve karte hain:
det(n adj (adj (mA)))=nm∣adj(adj(mA))∣
Step 3: a,b,c ki values nikalna
Hame expression ko 3a5b6c ke roop mein likhna hai.
Hum 25 ko adjust karne ke liye 35 se multiply aur divide kar sakte hain taaki 65 ban sake:
Iska comparison 3a5b6c se karne par:
Step 4: Final Answer
Sahi vikalp (4) 96 hai.
