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Prove that: |a^2+2a2a+1 1 2a+1a+2 1 3 3 ...

Prove that: `|a^2+2a2a+1 1 2a+1a+2 1 3 3 1|=(a-1)^3` .

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LHS $$ \left|\begin{array}{ccc} a^{2}+2 a & 2 a+1 & 1 \\ 2 a+1 & a+2 & 1 \\ 3 & 3 & 1 \end{array}\right| $$ ...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
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  3. Prove that: |a^2+2a2a+1 1 2a+1a+2 1 3 3 1|=(a-1)^3 .

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  7. If m in N and mgeq2 prove that: |1 1 1\ ^m C1\ ^(m+1)C1\ ^(m+2)C1\ ^m...

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  15. Prove that: |(b+c)^2a^2a^2b^2(c+a)^2b^2c^2c^2(a+b)^2|=2a b c(a+b+c)^3

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  16. Prove that: |(a,b, ax+by),(b,c,bx+cy), (ax+by, bx+cy,0)|=(b^2-a c)(a x...

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  17. Without expanding the determinant, show that (a+b+c) is a factor of...

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  18. If a ,\ b ,\ c are roots of the equation x^3+p x^{2}+q=0 , prove tha...

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  19. If a, b, c are positive and unequal, show that value of the determinan...

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  20. If a+b+c!=0 and |a b c b c a c a b|=0 , then prove that a=b=c dot

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