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Prove that : |b c-c^2c a-^2a b-c^2c a-b^...

Prove that : `|b c-c^2c a-^2a b-c^2c a-b^2a b-c^2b c-a^2a b-c^2b c-a^2c a-b^2|=|a b c b c a c a b|^2`

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Prove that: |[b, c-a^2,c] ,[a-b^2,a b-c^2,c ],[a-b^2,a ,b-c^2b c-a^2a b-c^2b c-a^2c a-b^2]|=|[a, b, c],[ b ,c ,a],[ c, a ,b]|^2 .

Prove that: |(b+c)^2a^2a^2b^2(c+a)^2b^2c^2c^2(a+b)^2|=2a b c(a+b+c)^3

Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c a=(a-b)^2+(b-c)^2+(c-a)^2

Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c a=[(a-b)^2+(b-c)^2+(c-a)^2]

Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c a=[(a-b)^2+(b-c)^2+(c-a)^2]

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

Show that: |(b+c)^2b a c a a b(c+a)^2c b a c b c(a+b)^2|=2a b c(a+b+c)^3

Show that: |b^2+c^2a b a c b a c^2+a^2b c c a c b a^2+b^2|=4a^2b^2c^2

Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a b c(a+b+c)^3

Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a b c(a+b+c)^3

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. if =|{:(x^(n),,n!,,2),(cos x,,cos.(npi)/(2),,4),(sin x,,sin .(npi)/(2)...

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  2. Without expanding a determinant at any stage, show that abs((x^2+x ,x+...

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  3. Prove that : |b c-c^2c a-^2a b-c^2c a-b^2a b-c^2b c-a^2a b-c^2b c-a^2c...

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  4. Show that the system of equations 3x-y + 4z = 3, x + 2y-3z =-2 and 6x ...

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  5. Let Delta = |{:(-bc,,b^(2)+bc,,c^(2)+bc),(a^(2)+ac,,-ac,,c^(2)+ac),(a^...

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  6. If y=|sinxcosxsinxcosx-sinxcosxx1 1|=fin d(dy)/(dx)dot

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  7. Consider the system of equation x+y+z=6,x+2y+3z=10 ,a n dx+2y+lambdaz=...

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  8. Consider the system linear equations in x ,y ,a n dz given by (sin3th...

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  9. Prove without expansion that |a h+bgga b+c h bf+b afh b+b c af+b cc bg...

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  10. If alpha,beta "and" gamma are real number without expanding at any sta...

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  11. If 3 digit numbers A28, 3B9 and 62C are divisible by a fixed constant ...

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  12. If a=costheta+isintheta,b=cos2theta-isin2theta,c=cos3theta+i sin3theta...

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  13. Prove that |[a1alpha1+b1beta1, a1alpha2+b1beta2, a1alpha3+b1beta3], [a...

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  14. If alpha,beta,gamma are the roots of p x^3+q x^2+r=0, then the value o...

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  15. prove that |{:((a-x)^(2),,(a-y)^(2),,(a-z)^(2)),((b-x)^(2),,(b-y)^(2),...

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  16. If |[1, x, x^2], [x, x^2, 1], [x^2, 1, x]|=3, then find the value ...

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  17. If |[x^n, x^(n+2), x^(n+3)], [y^n, y^(n+2), y^(n+3)], [z^n, z^(n+2), z...

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  18. Solve the system of the equations: a x+b y+c z=d, a^2x+b^2y+c^2z=d^2,...

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  19. If |[a,b-c,c+b],[a+c,b,c-a],[a-b,a+b,c]|=0 , then the line a x+b y+c=0...

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  20. If 2a x-2y+3z=0,x+a y+2z=0,a n d, 2x+a z=0 have a nontrivial solutio...

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