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Using properties of determinants, prove that `|b+c q+r y+z c+a r+p z+x c+b p+q x+y|=2\ |a p x b q y c r z|`

A

`Delta=2Delta_(1)`

B

`Delta=-2Delta_(1)`

C

`Delta=4Delta_(1)`

D

`Delta=-4Delta_(1)`

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A
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MCGROW HILL PUBLICATION-DETERMINANTS-SOLVED EXAMPLES (LEVEL 1 SINGLE CORRECT ANSWER TYPE QUESTIONS)
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  2. If 1,omega , omega^2 are the cube roots of unity , then Delta=|(1,ome...

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  3. Using properties of determinants, prove that |b+c q+r y+z c+a r+p ...

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  4. If x=-2 and Delta=|(x+y,x,x),(5x+4y,4x,2x),(10x+8y,8x,3x)| then numeri...

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  5. If a=omega!=1, is a cube root of unity b=785,c=2008i and Delta=|(a,a...

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  6. for x,x,z gt 0 Prove that |{:(1,,log(x)y,,log(x)z),(log(y)x,,1,,log(y)...

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  7. Let omega!=1 be a cube root of unit and Delta=|(1-omega-omega^(2),2,...

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  8. Suppose x=-1/3(1+sqrt(7)i) and y="cos"(pi)/4+I"sin"(pi)/4 Let Delta=...

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  9. Let x="cos"(pi)/3+i "sin"(pi)/3 and Delta=|(1,x,x^(2)),(x^(2),1,x),(...

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  10. Let f(x)=[2^(-x^(2))[2x^(2)]],x epsilon R ( [ ] denotes the greatest i...

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  11. If omega!=1 is a cube root of unity and Delta=|(x+omega^(2),omega,1)...

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  12. Let f:NtoN be defined by f(x)=(x+1)^(2)+x-[sqrt((x+1)^(2)+(x+1))]^(2...

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  13. If x=-9 is a root of |(x,3,7),(2,x,2),(7,6,x)|=0 then other two roots ...

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  14. Delta(1)=|{:(x,b,b),(a,x,b),(a,a,x):}| and Delta(2)=|{:(x,b),(a,x):}| ...

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  15. If x in R and n in I then the determinant Delta= |[sin(npi), sinx-cosx...

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  16. Prove that |{:(ax,,by,,cz),(x^(2),,y^(2),,z^(2)),(1,,1,,1):}|=|{:(a,,...

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  17. If f(x)=|{:(1,x,x+1),(2x,x(x-1),(x+1)x),(3x(x-1),x(x-1)(x-2),(x+1)x(x-...

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  18. If Delta(x)=|(1,1,1),((e^(x)+e^(-x))^(2),(pi^(x)+pi^(-x))^(2),2),((e^(...

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  19. If Delta (x)=|{:(1,cos x,1-cos x),(1+sin x,cos x,1+sinx-cosx),(sinx,si...

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  20. The determinant Delta=|{:(a,b,aalpha+c),(b,c,balpha+c),(aalpha+b,balph...

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