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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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$$ \Delta=\left|\begin{array}{ccc} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \end{array}\right| $$ Applying `R_{1} \rightarrow R_{1}+R_{2}`, we have: ...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. If w is a complex cube root of unity. Show that |1w w^2w w^2 1w^2 1...

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  2. Show that |1a b+c1b c+a1c 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 |1b c a(b+c)1c a b(c+a)1a b c(a+b)|=0 .

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  5. Without expanding prove that: |x+y y+z z+x z x y1 1 1|=0 .

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  6. Without expanding show that: =|cos e c^2thetacot^2theta1cot^2thetac...

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  7. Find the value of the determinant =|2 3 4 5 6 8 6x9x 12 x| .

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  8. Without expanding show that |b^2c^2b c b+cc^2a^2c a 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 |(x^2+x^(-1))^2(a^2-a^(-1))...

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  11. If a ,\ b ,\ c are in A.P., find the value of |2y+4 5y+7 8y+a3y+5 6...

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  12. Without expanding evaluate the determinant =|265 240 219 240 225 19...

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  13. 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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  14. 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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  15. 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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  16. If A is a skew-symmetric matrix of odd order n , then |A|=O .

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  17. Prove that: |0a-b-a0-c b c0|=0 .

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  18. Without expanding or evaluating show that |0b-a c-a a-b0c-b a-c b-c...

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  19. 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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  20. 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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