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

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

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Without expanding or evaluating show that |[0 , b-a , c-a] , [a-b , 0 , c-b] , [a-c , b-c , 0]|=0

Using the property of determinants and without expanding, prove that: |[a-b,b-c,c-a],[ b-c,c-a ,a-b ],[c-a ,a-b,b-c]|=0

If a, b and c are real numbers, and Delta=|[b+c,c+a,a+b],[c+a,a+b,b+c],[a+b,b+c,c+a]|=0 . Show that either a+b+c=0 or a=b=c

Show that |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b ,c(a+b)]|=0 .

Without expanding or evaluating show that |(0,b-a, c-a),( a-b,0,c-b),( a-c ,b-c,0)|=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)

Prove the identities: |[a, b-c,c-b],[ a-c, b, c-a],[ a-b,b-a, c]| =(a+b-c)(b+c-a)(c+a-b)

Show that |[1,a,a^2],[1,b,b^2],[1,c,c^2]|=(a-b)(b-c)(c-a)

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: |[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

RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If w is a complex cube root of unity. Show that |[1,w, w^2],[w, w^2,...

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  2. Show that |[1,a ,b+c],[1,b, c+a],[1,c ,a+b]|=0 .

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

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  4. Show that |[1,b c, a(b+c)],[1,c a, b(c+a)],[1,a b ,c(a+b)]|=0 .

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  5. Without expanding prove that: |[x+y, y+z, z+x],[z ,x, y],[1, 1 ,1]|=...

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  6. Without expanding show that: =|[cose c^2theta,cot^2theta,1],[cot^2th...

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  7. Find the value of the determinant =|(2, 3, 4) ,(5, 6, 8),( 6x,9x, 12...

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  8. Without expanding show that |b^2c^2 bc b+cc^2a^2 ca c+a a^2b^2a b a+...

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  9. Without expanding evaluate the determinant |sinalphacosalphasin(alp...

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  10. Without expanding evaluate the determinant |(a^x+a^-x)^2(a^x-a^-x)^2 1...

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  11. If a ,\ b ,\ c are in A.P., find the value of |(2y+4, 5y+7, 8y+a),(3...

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  12. Without expanding evaluate the determinant =|(265, 240, 219), (240, ...

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  13. If D1=|1 1 1 x^2 y^2 z^2 x y z| and D2=|1 1 1y z z xx y x y z| , with...

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  14. Let D=|Ax x^2 1 By y^2 1 Cz z^2 1| and D1=|A B C x y z yz zx xy| ...

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  15. If A=|[a, b, c],[ x, y, z],[ p, q, r]| and B=|[q, -b, y],[ -p, a, -x...

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  16. If A is a skew-symmetric matrix of odd order n , then |A|=O .

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  17. Prove that: |[0,a,-b],[-a,0,-c],[ b, c,0]|=0 .

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  18. Without expanding or evaluating show that |(0,b-a, c-a),( a-b,0,c-b)...

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  19. Without expanding, prove that |(a+b x, c+dx, p+q x), (a x+b, c x+d, ...

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  20. Prove that: |-a^2 ab ac ba -b^2 bc ...

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