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Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b]...

Prove that `|[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-c^3dot`

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Using properties of determinants. Prove that |[3a,-a+b,-a+c], [-b+a,3b,-b+c], [-c+a,-c+b,3c]|=3(a+b+c)(a b+b c+c a)

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Prove that the value of each the following determinants is zero: |s...

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  2. The number of values of k for which the system of the equations (k+1)x...

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  3. Prove that |[b+c ,a-b, a] ,[c+a, b-c ,b],[ a+b, c-a, c]|=3abc-a^3-b^3-...

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  4. " if " |{:(a^(2),,b^(2),,c^(2)),((a+1)^(2),,(b+1)^(2),,(c+1)^(2)),((a-...

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  5. Bond energies can be obtained by using the following relation: DeltaH ...

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

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  7. If =|s inthetacosvarphisinthetas invarphicosthetacosthetacosvarphicost...

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  8. The system of equations -2x+y+z=a, x-2y+z=b, x+y-2z=c, has: (a)no so...

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  9. Show that if x1, x2, x3!=0 |x1+a1b1a1b2a1b3a2b1x2+a2b2a2b3a3b1a3b2x3+...

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  10. Figure shows a wire ring of radius a that is perpendicular to the gene...

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  11. If Deltar =|[2^(r-1) ,2.3^(r-1), 4.5^(r-1)],[alpha,beta,gamma],[2^n-1,...

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  12. The values of k in R for which the system of equations x+k y+3z=0,k x...

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  13. A determinant of second order is made with the elements 0 and 1. Fi...

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  14. For a concave mirror, if real image is formed the graph between (1)/(u...

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  15. Prove that the determinant |[x, sintheta,costheta],[-sintheta,-x,1],[...

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  16. Consider the determinant f(x)=|0x^2-a x^3-b x^2+a0x^2+c x^4+b x-c0|dot...

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  17. Find the value of |[1, 2, 4],[-1,3, 0],[4 ,1, 0]|

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  18. Consider the system of the equation k x+y+z=1,x+k y+z=k ,a n dx+y+k z=...

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  19. If x+y+z=0 prove that |[a x, b y, c z],[ c y, a z ,b x],[ b z ,c x ,a ...

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  20. Each question has four choices a, b, c and d, out of which only one is...

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