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Prove |[-bc, b^2+bc, c^2+bc] , [a^2+ac, ...

Prove `|[-bc, b^2+bc, c^2+bc] , [a^2+ac, -ac, c^2+ac] , [a^2+ab, b^2+ab, -ab]|`=`(ab+bc+ca)^2`

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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)

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)) |:}

Prove that |(-a^2,ab,ac),(bc,-b^2,bc),(ca,cb,-c^2)|=4a^(2)b^(2) c^(2) .

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

Prove that abs{:(a^(2) + 1, ab , ac),(ab, b^(2) + 1, bc),(ca, cb, c^(2) +1):}=1 + a^(2) + b^(2) +c^(2)

Using the property of determinants and without expanding prove that {:|( -a^(2) , ab,ac),( ba,-b^(2) , bc) ,( ca, cb, -c^(2)) |:} =4a^(2) b^(2) c^(2)

Find the product (2a + b+c) (4a ^(2) + b ^(2) + c ^(2) - 2ab -bc -2ca)

|(a^(2)+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)|= 1 + a^2 + b^2 + c^2 .

|(b^(2)c^(2),bc,b+c),(c^(2)a^(2),ca,c+a),(a^(2)+b^(2),ab,a+b)|=

Prove that =ab+bc+ca+abc

OSWAAL PUBLICATION-DETERMINANTS-TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTIONS-I)
  1. Prove that : |{:(a,b,c),(a^(2),b^(2),c^(2)),(bc,ca,ab):}|=(a-b)(b-c)(c...

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

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

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

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

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  6. [[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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  7. 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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  8. 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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  9. Using properties of determinants, prove that |b+c q+r y+z c+a r+p ...

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  10. Using the Properties of determinants, prove that following: {:|(-a^2...

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  11. Using the Properties of determinants, prove the following: {:|(1,1...

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  12. If |{:(x,x^2,1+x^3),(y,y^2,1+y^3),(z, z^2,1+z^3):}|=0 and x, y, z are ...

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  13. Using properties of determinants, solve the following for x: |x-2 ...

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  14. Using properties of determinants, solve for x:|a+x a-x a-x a-x a+x a...

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  15. Using Properties of determinants, solve the following for x: {:|(x+a...

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  16. Prove, using properties of determinants: |y+k y y y y+k y y y y+k|=k^...

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  17. Prove |[-bc, b^2+bc, c^2+bc] , [a^2+ac, -ac, c^2+ac] , [a^2+ab, b^2+ab...

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

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  19. |(b+c,c+a,a+b),(c+a,a+b,b+c),(a+b,b+c,c+a)|=2(3abc-a^(3)-b^(3)-c^(3))

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  20. Prove, using Properites of determinants, {:|(a+bx^2,c+dx^2,p+qx^2),(...

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