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Evaluate: |1a a^2 1bb^2 1cc^2| ....

Evaluate: `|1a a^2 1bb^2 1cc^2|` .

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The correct Answer is:
`=(a-b)(b-c)(c-a)`
ATQ, it is given: $$ \begin{aligned} &\left|\begin{array}{ccc} 1 & a & a^{2} \\ 1 & b & b^{2} \\ 1 & c & c^{2} \end{array}\right| \\ \\ ...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
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  2. Prove that: |1 1 1 1 1+x1 1 1 1+y|=x y .

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  3. Evaluate: |1a a^2 1bb^2 1cc^2| .

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  4. Show that : |x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot

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  10. For any scalar p prove that =|xx^2 1+p x^3y y^2 1+p y^3z z^2 1+p z^3|=...

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  11. Using properties of determinants, show that |1a a^2-b c1bb^2-c a1cc...

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

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  13. Let a ,\ b and c denote the sides B C ,\ C A and A B respectively of ...

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

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  19. Show that: |1 1+p1+p+q2 3+2p1+3p+2q3 6+3p1+6p+3q|=1 .

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  20. Show that: |a a+b a+b+c2a3a+2b4a+3b+2c3a6a+3b 10 a+6b+3c|=a^3 .

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