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" if " Delta = |{:(-x,,a,,b),(b,,-x,...

` " if " Delta = |{:(-x,,a,,b),(b,,-x,,a),(a,,b,,-x):}|" then a factor of " Delta " is "`

A

a+b-x is a factor of `Delta`

B

`x^(2)+(a+b)x+a^(2)+b^(2)-ab"is a factor of "Delta`

C

`Delta=0` has three real roots if `a=b`

D

a+b+x is a factor of `Delta`

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A, B, C
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RESONANCE ENGLISH-MATRICES & DETERMINANT-PART-III
  1. Which one of the following is wrong?

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  2. Which of the following is true for matrix A=[{:(,1,-1),(,2,3):}]

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  3. Suppose a(1),a(2),a(3) are in A.P. and b(1),b(2),b(3) are in H.P. and ...

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  4. Let theta=(pi)/(5),X=[{:(,cos theta,-sin theta),(,sin theta,cos theta)...

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  5. If Delta=|{:(,x,2y-z,-z),(,y,2x-z,-z),(,y,2y-z,2x-2y-z):}|,then

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  6. " if " Delta = |{:(-x,,a,,b),(b,,-x,,a),(a,,b,,-x):}|" then a fac...

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  7. the determinant |{:(a,,b,,aalpha+b),(b,,c,,balpha+c),(aalpha+b,,balpha...

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  8. The determinant Delta=|{:(,a^(2)(1+x),ab,ac),(,ab,b^(2)(1+x),(bc)),(,a...

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  9. If a non-singular matrix and A^(T) denotes the tranpose of A, then

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  10. Let "Let"(x)=|{:(,2sinx,sin^(2)x,0),(,1,2sin x,sin^(2)x),(,0,1,2sin x)...

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  11. Let Delta=|{:(,1,x,x^(2)),(,x^(2),1,x),(,x,x^(2),1):}|. Then

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  12. Let f(x)=|{:(,1//x,logx,x^(n)),(,1,-1//n,(-1)^(n)),(,1,a,a^(2)):}| whe...

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  13. If D is determinant of order three of Delta is a determinant formed by...

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  14. Let A,B,C,D be real matrices such that A^(T)=BCD,B^(T)=CDA,C^(T)=DAB a...

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  15. Let A and B be two 2 xx 2 matrix with real entries, If AB=0 and such t...

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  16. If A^(-1)=[{:(,1,-1,0),(,0,-2,1),(,0,0,-1):}] then

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  17. IF A and B are squre matrices of order 3, then the true statement is/a...

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  18. Let M be a 3xx3 non-singular matrix with det(M)=4,"If" M^(-1)"adj(adjM...

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