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

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

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

Using the Properties of determinants, prove that following: {:|(-a^2,ab,ac),(ba,-b^2,bc),(ac,bc,-c^2)|=4a^2b^2c^2

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)

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

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)

If |(-a^2,ab,ac),(ab,-b^2,bc),(ac,bc,-c^2)|=lamdaa^2b^2c^2 then the value of lamda is :

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

If a^2+b^2+c^2=0 and |(b^2+c^2,ab,ac),(ab,c^2+a^2,bc),(ac,bc,a^2+b^2)|=ka^2b^2c^2 , then the value of k is :

OSWAAL PUBLICATION-DETERMINANTS-TOPIC -1 DETERMINANTS, MINORS & COFACTORS (LONG ANSWER TYPE QUESTIONS-I)
  1. Prove: |2y y-z-x2y2z2z z-x-y x-y-z2x2x|=(x+y+z)^3

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

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

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

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

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

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

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

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

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

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

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  14. [[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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  15. 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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  16. 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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  17. Using properties of determinants, prove that |b+c q+r y+z c+a r+p ...

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

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

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  20. 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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