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

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`

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Explore conceptually related problems

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)^2a^2a^2b^2(c+a)^2b^2c^2c^2(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 cc a c b a^2+b^2|=4a^2\ b^2\ c^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

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

Prove: |((b+c)^2, a^2, b c) ,((c+a)^2, b^2 ,c a),( (a+b)^2, c^2, a b)|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2) .

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 .

Without expanding show that |[b^2c^2,b c, b+c],[c^2a^2,c a ,c+a ],[a^2b^2,a b ,a+b]|=0

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

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If a ,\ b ,\ c are the roots of the equation x^3+p x+q=0 , then find...

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  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

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  3. 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)...

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  4. 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^...

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

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  6. Prove that: |a b a x+b y b c b x+c y a x+b y b x+c y0|=(b^2-a c)(a x^2...

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  7. Without expanding the determinant, show that (a+b+c) is a factor of ...

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  8. If a ,\ b ,\ c are roots of the equation x^3+p x+q=0 , prove that d...

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  9. Find dy/dx if y=cos^2x

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  10. If a+b+c!=0 and , \begin{vmatrix} a & b & c \\ b & c & a \\ ...

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  11. If a , b , c are real numbers, prove that \begin{vmatrix} a & b & ...

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  12. Show that: |a b-cc+b a+c b c-a a-bb+a c|=(a+b+c)(a^2+b^2+c^2)dot

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

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  14. Using properties of determinants, solve for x:|[a+x, a-x, a-x], [a-x...

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  15. Using properties of determinants, solve the following for x: |[x-2,...

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  16. If a,b,c are all distinct and |[a,a^3,a^4-1],[b,b^3,b^4-1],[c,c^3,c^4-...

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  17. If a , b , c are all positive and are p t h ,q th and r t h terms of a...

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  18. If x+y+z=0 prove that | xa yb zc yc za xb zb xc ya y|=x y z|a b c...

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  19. 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 ...

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  20. Prove that: |[bc-a^2, ca-b^2,ab-c^2],[ca-b^2,ab-c^2,bc-a^2],[ab-c^2,bc...

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