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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
- If 1=|1 1 1x^2y^2z^2x y z| and 2=|1 1 1y z z xx y x y z| , without exp...
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- Let =|A xx^2 1B y y^2 1C z z^2 1| and 1=|A B C x y z y z z xx y| , the...
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- If 1=|a b c x y z p q r| and 2=|q-b y-p a-x r-c z| , without expanding...
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- If A is a skew-symmetric matrix of odd order n , then |A|=O .
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- Prove that: |0a-b-a0-c b c0|=0 .
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- Without expanding or evaluating show that |0b-a c-a a-b0c-b a-c b-c...
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- Without expanding, prove that |a+b x c+dx p+q x a x+b c x+d p x+q u...
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- Prove that: |-a^2a b a c b a-b^2b c a c b c-c^2|=4a^2b^2c^2 .
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- Prove that: |1 1 1 1 1+x1 1 1 1+y|=x y .
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- Evaluate: |1a a^2 1bb^2 1cc^2| .
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- Show that : |x y z x^2y^2z^2x^3y^3z^3|=x y z(x-y)(y-z)(z-x)dot
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- Prove that: |alphabetagammaalpha^2beta^2gamma^2beta+gammagamma+alphaal...
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- In a triangleABC, if |[1,1,1][1+sinA,1+sinB,1+sinC],[sinA+sin^2A,sinB+...
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- In a A B C ,if|1 1 1 1+cosA1+cosB1+cosCcos^2A+cosBcos^2A+cosBcos^2+co...
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- Show that |[a ,b ,c],[ a^2,b^2,c^2],[bc, ca, ab]|=|[1, 1, 1],[a^2,b^2,...
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- If x!=y!=z and |xx^2 1+x^3y y^2 1+y^3z z^2 1+z^3|=0 , then prove that ...
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- For any scalar p prove that =|xx^2 1+p x^3y y^2 1+p y^3z z^2 1+p z^3|=...
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- Using properties of determinants, show that |1a a^2-b c1bb^2-c a1cc...
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- Prove that: |a^2+2a2a+1 1 2a+1a+2 1 3 3 1|=(a-1)^3 .
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- Let a ,\ b and c denote the sides B C ,\ C A and A B respectively of ...
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