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Prove that : (i) |{:(a,c,a+c),(a+b,b,a...

Prove that :
(i) `|{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc`
(ii) Prove that : `|{:(a^(2),bc,ac+c^(2)),(a^(2)+ab,b^(2),ac),(ab,b^(2)+bc,c^(2)):}|=4a^(2)b^(2)c^(2)`

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OSWAAL PUBLICATION-DETERMINANTS-TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTIONS-I)
  1. Using properties of determinants, prove that |a+x y z x a+y z x y a+z...

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  2. Using Properties of determinants, prove that {:|(x+lamda,2x,2x),(2...

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  3. Prove that : (i) |{:(a,c,a+c),(a+b,b,a),(b,b+c,c):}|=2 abc (ii) Pr...

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  4. Prove: |2y y-z-x2y2z2z z-x-y x-y-z2x2x|=(x+y+z)^3

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  5. Using Properties of determinants, prove that: {:|(x^2+1,xy,yz),(xy,y...

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  6. Prove that: |(a^2+1, ab, ac),(ab, b^2+1, bc),(ac, bc, c^2+1)|=1+a^2+b^...

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  7. Using Properties of determinants, prove that {:|(x+y,x,x),(5x+4y,4x,...

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  8. Using Properties of determinants, prove that: {:|(b+c,c+a,a+b),(q+r,...

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  9. IF a+b+c ne 0 and {:|(a,b,c),(b,c,a),(c,a,b)|=0, then using properties...

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  10. Prove that |[1,a,a^3],[1,b,b^3],[1,c,c^3]|=(a-b)(b-c)(a+b+c)

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  11. Prove that: (i) |{:(,1,1,1),(,a,b,c),(,a^(3),b^(3),c^(3)):}|=(a-b)(b...

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  12. Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c...

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  13. Find the equation of the line joining A( 1,3) and B (0,0) using det...

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  14. Using properties of determinants, prove the following: |xx+y x+2y\...

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  15. Using properties of determinants, prove the following: |alphabetag...

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  16. 15. Using properties of determinants, prove the following |[a,b,c],[a-...

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  17. [[b+c,a-b,a],[c+a,b-c,b],[a+b,c-a,c]] = 3abc - a^3 - b^3 - c^3

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  18. Prove that |[a^2, a^2-(b-c)^2, bc],[b^2, b^2-(c-a)^2, ca],[c^2, c^2-(...

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  19. Prove that |(a,b-c,c+b),(a+c,b,c-a),(a-b,b+a,c)|=(a+b+c)(a^(2)+b^(2)...

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  20. Using properties of determinants, prove that |b+c q+r y+z c+a r+p ...

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