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Prove that |((b+x)(c+x),(c+x)(a+x),(a+x)...

Prove that `|((b+x)(c+x),(c+x)(a+x),(a+x)(b+x)),((b+y)(c+y),(c+y)(a+y),(a+y)(b+y)),((b+z)(c+z),(c+z)(a+z),(a+z)(b+z))|=(a-b)(b-c)(c-a)(x-y)(y-z)(z-x)dot`

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Prove that |(x+2a,y+2b,z+2c),(x,y,z),(a,b,c)|=0

Evaluate |{:(.^(x)C_(1),,.^(x)C_(2),,.^(x)C_(3)),(.^(y)C_(1),,.^(y)C_(2),,.^(y)C_(3)),(.^(x)C_(1),,.^(z)C_(2),,.^(z)C_(3)):}|

Solve that |(y+z,x,x^(2)),(z+x,y,y^(2)),(x+y,z,z^(2))|=(x+y+z)(x-y)(y-z)(z-x)

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c x+a z b z+c y c z-a x-b y|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

Prove that |{:(ax,,by,,cz),(x^(2),,y^(2),,z^(2)),(1,,1,,1):}|=|{:(a,,c,,c),(x,,y,,z),(yz,,xz,,xy):}|

|{:(.^(x)C_(r),,.^(x)C_(r+1),,.^(x)C_(r+2)),(.^(y)C_(r),,.^(y)C_(r+1),,.^(y)C_(r+2)),(.^(z)C_(r),,.^(z)C_(r+1),,.^(z)C_(r+2)):}| is equal to

CENGAGE-DETERMINANTS-All Questions
  1. Prove that [[1+a^2+a^4, 1+a b+a^2b^2 ,1+a c+a^2c^2],[ 1+a b+a^2b^2, 1+...

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  2. If x , y , z are in A.P. , then the value of the determinant are in A....

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  3. Prove that |((b+x)(c+x),(c+x)(a+x),(a+x)(b+x)),((b+y)(c+y),(c+y)(a+y),...

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  4. If a+b+c=0, one root of [[a-x, c, b],[c, b-x, a],[ b, a, c-x]]=0 is ...

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  5. Factorize the following |3a+b+c a^3+b^3+c^3a+b+c a^2+b^2+c^2a^4+b^4+ ...

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  6. Let {D1, D2, D3 ,Dn} be the set of third order determinant that can be...

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  7. If g(x)-(f(x))/((x-a)(x-b)(x-c)),w h e r ef(x) is a polynomial of d...

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  8. If the equation 2x+3y+1=0,3x+y-2=0,a n da x+2y-b=0 are consistent, ...

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  9. If w is a complex cube root of unity, then value of =|a1+b1w a1w^2+b1c...

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  10. Let f(x)=|cos(x+x^2)sin(x+x^2)- cos(x+x^2)...

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  11. Which of the following has/have value equal to zero? |8 2 7 12 3 5 16 ...

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  12. If f(x),g(x)a n dh(x) are three polynomials of degree 2, then prove th...

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  13. If a ,b ,c are in G.P. with common ratio r1a n dalpha,beta,gamma are...

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  14. Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

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  15. In triangle A B C , if |1 1 1cotA/2cotB/2cotC/2tanB/2+tanC/2tanB/2+tan...

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  16. If a ,b ,c ,d ,e, and fare in G.P. then the value of |((a^2),(d^2),x)...

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  17. Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a...

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  18. " if " x(i) =a(i) b(i) C(i) i= 1,2,3 are three- digit positive integer...

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  19. The system of linear equations x+lambday-z=0 lambdax-y-z=0 x+y-lambd...

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  20. If p q r!=0 and the system of equation (p+a)x+b y+c z=0 a x+(q+b)...

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