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Show that |{:( 2bc-a^2 , c^2 ,b^2),(c^2 ...

Show that `|{:( 2bc-a^2 , c^2 ,b^2),(c^2 , 2ca-b^2 , a^2),(b^2 , a^2 , 2ab-c^2):}| = |{:(a,b,c),(b,c,a),(c,a,b):}|^2`

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Show that |{:(bc-a^(2),,ca-b^(2),,ab-c^(2)),(ca-b^(2),,ab-c^(2),,bc-a^(2)),(ab-c^(2),,bc-a^(2),,ca-b^(2)):}| |{:(a^(2),,c^(2),,2ca-b^(2)),(2ab-c^(2),,b^(2),,a^(2)),(b^(2),,2ac-a^(2),,c^(2)):}|.

Show that |{:(b+c,bc,b^(2)c^(2)),(c+a,ca,c^(2)a^(2)),(a+b,ab,a^(2)b^(2)):}| = 0

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

Show that |(b+c,bc,b^(2)c^(2)),(c+a,ca,c^(2)a^(2)),(a+b,ab,a^(2)b^(2))|=0 .

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

If |{:(a,b,a),(b,c,1),(c,a,1):}|=2010 and if |{:(c-a,c-b,ab),(a-b,a-c,bc),(b-c,b-a,ca):}|-|{:(c-a,c-b,c^(2)),(a-b,a-c,a^(2)),(b-c,b-a,b^(2)):}|=p , then the number of positive divisors of p is

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) , bc, ac+c^(2)),( a^(2) +ab,b^(2) ,ac),( ab,b^(2) +bc,c^(2)) ]:} =4a^(2) b^(2) c^(2)

Prove that |{:(a,,a^(2),,bc),(b ,,b^(2),,ac),( c,,c^(2),,ab):}| |{:(1,,1,,1),(a^(2) ,,b^(2),,c^(2)),( a^(3),, b^(3),,c^(3)):}|

Show that (a^(2)+b^(2),c^(2)),(b^(2)+c^(2),a^(2)) ,and (c^(2)+a^(2),b^(2)) are collinear

CENGAGE-DETERMINANTS-All Questions
  1. Show that |{:(bc-a^(2),,ca-b^(2),,ab-c^(2)),(ca-b^(2),,ab-c^(2),,bc-a^...

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

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  3. Show that |{:( 2bc-a^2 , c^2 ,b^2),(c^2 , 2ca-b^2 , a^2),(b^2 , a^2 , ...

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

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

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  6. Consider the system of linear equations in x , ya n dz : ""(sin3theta...

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

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

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

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

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  11. Prove that |a1alpha1+b1beta1a1alpha2+b2beta2a1alpha3+b1beta3a2alpha1+b...

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

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  13. Prove that |(a-x)^2(a-y)^2(a-z)^2(b-x)^2(b-y)^2(b-z)^2(c-x)^2(c-y)^2(...

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  14. If |1xx^2xx^2 1x^2 1x|=, then find the value of |x^3-1 0x-x^4 0x-x^...

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  15. If |x^n x^(n+2)x^(n+3)y^n y^(n+2)y^(n+3)z^n z^(n+2)z^(n+3)|=(x-y)(y-z)...

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

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  17. if |{:(a,,b-c,,c+b),(a+c,,b ,,c-a),(a-b,,a+b,,c):}|=0 then the line ...

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  18. If 2a x-2y+3z=0,x+a y+2z=0,a n d2+a z=0 have a nontrivial solution,...

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  19. If |.| denotes the greatest integer less than or equal to the real num...

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  20. if (x) =a +bx+cx^(2)" and " alpha, beta gamma are the roots of the ...

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