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Show that: |[3a,-a+b,-a+c],[-b+a,3b,-b+c...

Show 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)dot`

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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)

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)

Show that: |3a-a+b-a+c-b+a3b-b+c-c+a-c+b3c|=3(a+b+c)(a b+b c+c a)dot

Show that |[b-c,c-a, a-b],[ c-a, a-b,b-c],[ a-b,b-c,c-a]| = 0 .

Show that |[a, b-c, c+b] , [a+c, b, c-a] , [a-b, b+a, c]|=(a+b+c)(a^2+b^2+c^2)

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

Show that: |a, b-c,c+b, a+c, b, c-a,a-b,b+a, c|=(a+b+c)(a^2+b^2+c^2)dot

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

Show that: |[a, a+b ,a+b+c],[2a,3a+2b,4a+3b+2c],[3a,6a+3b, 10 a+6b+3c]|=a^3 .

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

CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. By using properties of determinants. Show that: |1+a^2-b^2 2a b-2b2a b...

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

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  3. 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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  4. 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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  5. 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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  6. The value of |[yz, z x,x y],[ p,2q,3r],[1, 1, 1]| , where x ,y ,z are ...

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

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

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

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

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

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  13. 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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  14. If =|s inthetacosvarphisinthetas invarphicosthetacosthetacosvarphicost...

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

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

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

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

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

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

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