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प्रश्न
Without actual expansion show that the value of the determinant `|(5,5^2,5^3),(5^2,5^3,5^4),(5^4,5^5,5^6)|` is zero.
उत्तर
Taking 5, 52 and 54 common from R1, R2 and R3 respectively we get
`|(5,5^2,5^3),(5^2,5^3,5^4),(5^4,5^5,5^6)| = 5 xx 5^2 xx 5^4 |(1,5,5^2),(1,5,5^2),(1,5,5^2)|`
= 5 × 5^2 × 5^4 × 0 = 0 ....[R1 ≡ R2 ≡ R3]
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