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Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2...

Prove that `|(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)`

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Prove that |(1,a^2,bc),(a,b^2,ca),(1,c^2,ab)|=(a-b)(b-c)(c-a)

a. Minimize z =-3x+4y subject to constraints. x+2yle8 3x+2yle12 xge0, yge0 by graphical method. b. Prove that {:abs((1,a,a^2),(1,b,b^2),(1,c ,c^2)):} = (a - b)(b-c)(c-a)

Prove that {:[(1,ab,a+b),(1,bc,b+c),(1,ca,c+a):}]=(a-b)(b-c)(c-a)

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

Prove that |(1,1,1),(a,b,c),(a^(3),b^(3),c^(3))|=(a-b)(b-c)(c-a)(a+b+c)

Prove that |(1,1,1),(bc,ca,ab),(b+c, c+a, a+b)| = (a-b)(b-c)(c-a)

Using the Properties of determinants, prove the following: {:|(1,1,1),(a,b,c),(bc,ca,ab)|=(a-b)(b-c)(c-a)

Using the property of determinants and without expanding prove that {:|( 1,bc,a(a+c) ),(1,ca,b( c+a)) ,( 1,ab,c(a+b) )|:}=0

Without expanding the determinant, prove that {:|( a, a ^(2), bc ),( b ,b ^(2) , ca),( c, c ^(2) , ab ) |:} ={:|( 1, a^(2) , a^(3) ),( 1,b^(2) , b^(3) ),( 1, c^(2),c^(3)) |:}

OSWAAL PUBLICATION-DETERMINANTS-TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTIONS-I)
  1. |[1+a^2-b^2,2ab,-2b],[2ab,1-a^2+b^2,2a],[2b,-2a,1-a^2-b^2]|=(1+a^2+b^2...

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  2. Show that |{:(1+a^(2)-b^(2),,2ab,,-2b),(2ab,,1-a^(2)+b^(2),,2a),(2...

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  3. Prove that |(1,a,a^2),(1,b,b^2),(1,c,c^2)|=(a-b)(b-c)(c-a)

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  4. |[b+c, a,a] , [b,c+a,b] , [c,c,a+b]|=4abc

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  5. Using properties of determinants, prove that |a+x y z x a+y z x y a+z...

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

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

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

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

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

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

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

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

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

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

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

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

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

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