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Prove that: {:|(a^2+2a,2a+1,1), (2a+1,a+...

Prove that: `{:|(a^2+2a,2a+1,1), (2a+1,a+2,1),(3,3,1)|:}=(a-1)^3` .

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ALLEN -DETERMINANTS-All Questions
  1. Prove that: |[ax,by,cz], [x^2,y^2,z^2], [1,1,1]|=|[a,b,c],[x,y,z],[yz,...

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  2. Prove that: {:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0

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  3. Prove that: {:|(a^2+2a,2a+1,1), (2a+1,a+2,1),(3,3,1)|:}=(a-1)^3 .

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  4. Using properties of determinants or otherwise evaluate {:|(18, 40, 8...

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  5. Using the property of determinants andd without expanding in following...

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  6. Using the properties of determinants, prove the following |{:(a,b-c,...

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  7. Absolute value of sum of roots of the equation {:|(x+2,2x+3,3x+4), (2x...

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  8. If a+b+c=0 and |{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 then find the val...

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  9. Suppose three digit numbers A28 , 3B9 and 52C , where A,B and C are in...

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  10. For a fixed positive integer n , if =|n !(n+1)!(n+2)!(n+1)!(n+2)!(n+3)...

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  11. If Dr=|2^(r-1)2(3^(r-1))4(5^(r-1))x y z2^n-1 3^n-1 5^n-1| then p...

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  12. Prove that |((beta+gamma-alpha-delta)^4,(beta+gamma-alpha-delta)^2,1),...

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  13. Solve the following sets of equations using Cramer's rule and remark a...

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  14. Solve the following sets of equation using Cramers rule and remark ...

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  15. Solve the following sets of equation using Cramers rule and remark ...

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  16. Solve the following sets of equation using Cramers rule and remark ...

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  17. Find those values of c for which the equations: 2x+3y=3,(c+ 2)x + (c +...

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  18. Let alpha1,alpha2a n d\ beta1,beta2 be the roots of a x^2+c=0\ a...

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  19. Prove that: {:|(1,a, a^2-bc), (1,b,b^2-ca),(1,c,c^2-ab)|:}=0

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  20. If Sr = alpha^r + beta^r + gamma^r then show that |[S0,S1,S2],[S1,S2,S...

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