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By using properties of determinants. Sho...

By using properties of determinants. Show that: `|1+a^2-b^2 2a b-2b2a b1-a^2+b^2 2a2b-2a1-a^2-b^2|=(1+a^2+b^2)^3`

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By using properties of determinants. Show that: |[1+a^2-b^2, 2a b,-2b],[2a b,1-a^2+b^2, 2a],[2b,-2a,1-a^2-b^2]|=(1+a^2+b^2)^3

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Show that |[1,1+p,1+p+q],[2,3+2p,1+3p+2q],[3,6+3p,1+6p+3q]|= 1

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  2. The determinant |a b aalpha+bb c balpha+c aalpha+bbalpha+c0|=0, if a ...

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  3. By using properties of determinants. Show that: |1+a^2-b^2 2a b-2b2a b...

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  4. Which of the following values of alpha satisfying the equation |(1+alp...

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  5. Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c],[-c+a,-c+b,3c]|=3(a+b+c)(a b...

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  6. If the system of equations x+a y=0,a z+y=0,a n da x+z=0 has infinite s...

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  7. If |[6i,-3i,1],[ 4, 3i,-1],[ 20, 3,i]|=x+i y , then a.x=3,y=1 b. x=1,y...

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  8. The value of |[yz, z x,x y],[ p,2q,3r],[1, 1, 1]| , where x ,y ,z are ...

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  9. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

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  10. Prove that the value of each the following determinants is zero: |s...

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

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

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

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  15. 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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  16. If =|s inthetacosvarphisinthetas invarphicosthetacosthetacosvarphicost...

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

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

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

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

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