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Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2...

Prove that `|(1,x,x^2),(1,y,y^2),(1,z,z^2)| = (x-y)(y-z)(z-x)`

A

(x-y)(y-z)(z-x)

B

2xyz

C

`(x+y+z)^2`

D

None of these

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PRADEEP PUBLICATION-DETERMINANTS-EXERCISE
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  2. True or False : Let A be a square matrix of order nge2 and B be the ...

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  3. True or False : The determinant of an identity matrix is always 1.

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  4. True or False : If A is a square matrix of order 1xx1 then adj A = O

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  5. Determinant of the 1xx1 matrix [-3] is

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  6. Determinant of the matrix A = [1,3,-5] is

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  7. The value of det [(cos theta, sintheta),(-sintheta, costheta)] is equa...

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  8. If A and B are invertible matrices of the same order, then (AB)^-1 is ...

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  9. A square matrix A invertible iff det A is equal to

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  10. If A is any of square matrix of order n, then A (adj A) is equal to

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  11. Prove that |(1,x,x^2),(1,y,y^2),(1,z,z^2)| = (x-y)(y-z)(z-x)

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  12. If A is a square matrix of order n, then det |lambdaA| is equal to (la...

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  13. If A is square matrix such that A^2 = I, then A ^-1 is equal to

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  14. If A is a square matrix of order 2, then det (adj A) is equal to

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  15. If A is a square matrix of order 2, then adj (adj A)

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  16. If A,B,C are three square matrices of the same order such that A= B +C...

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  17. If A = diag (d1,d2,d3,….dn) then det A is equal to

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  18. The area of a triangle with vertices (-3,0),(3,0) and (0,k) is 9 sq. u...

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  19. The equations {:(x+y+2=0),(2x+2y=3):} have

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  20. For what value of lambda, the following system of equations {:(x+y+z =...

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