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Without actual expansion, prove that the...

Without actual expansion, prove that the following determinants vanish :
`|{:(x+y,y+z,z+x),(z,x,y),(1,1,1):}|`

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MODERN PUBLICATION-DETERMINANTS-Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (I))
  1. Using the property of determinants and without expanding, prove that |...

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  2. Without actual expansion, prove that the following determinants vanish...

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  3. Using the property of determinants and without expanding in questions ...

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  4. Prove that |{:(1, a, a^(2)-bc),(1, b, b^(2)-ca), (1, c, c^(2)-ab):}|=...

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  5. witout expanding at any stage Prove that |{:(0,,a,,-b),(-a,,0,,-...

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  6. Without actual expansion, prove that the following determinants vanish...

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  7. The value of the determinant |{:(1,bc,a(b+c)),(1,ca,b(a+c)),(1, ab,c(a...

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  8. Without expanding the determinants show that : ((1)/(a)+(1)/(b)+(1)/...

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  9. Prove that : |{:(x-y-z,2x,2x),(2y,y-z-x,2y),(2z,2z,z-x-y):}|

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  10. Without expanding the determinant, prove that |a a^2b c bb^2c a cc^2a ...

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  11. Show without expanding at any stage that: [0,sinalpha-cosalpha],[-sin...

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  12. " If " |{:(x^(2)+x,,x+1,,x-2),(2x^(2)+3x-1,,3x,,3x-3),(x^(2)+2x+3,,2x...

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  13. Evaluate the following : |{:(b+c,a,a),(b,c+a,b),(c,c,a+b):}|

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  14. Evaluate the following : |{:(x+lambda,x,x),(x,x+lambda,x),(x,x,x+lam...

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  15. Evaluate the following: |[1, a, b+c],[1, b, c+a],[1, c, a+b]|

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  16. Evaluate: [[x,y,x+y],[y,x+y,x],[x+y,x,y]]

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  17. Evaluate the following: |[1,x,y],[1, x+y, y],[1, x, x+y]|

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  18. Prove that: |[b+c, c=a, a+b],[q+r, r+p, p+q],[y+z, z+x, x+y]|=2|[a,b,...

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  19. Use the properties of determinant and without expanding prove that |...

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