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The determinant Delta=|{:(cos(x+y),-sin(...

The determinant `Delta=|{:(cos(x+y),-sin(x+y),cos2y),(sinx,cosx,siny),(-cosx,sinx,cosy):}|` is independent of x only.

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ACCURATE PUBLICATION-DETERMINANTS-Type-III (True or False questions)
  1. The determinant Delta=|{:(cos(x+y),-sin(x+y),cos2y),(sinx,cosx,siny),(...

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  2. The value of |{:(1,1,1),(.^(n)C(n),.^(n+2)C(1),.^(n+4)C(1)),(.^(n)C(2)...

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  3. If A=[{:(x,5,2),(2,y,3),(1,1,z):}], xyz=80, 3x+2y+10z=20, then A adj *...

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  4. If A=[{:(0,1,3),(1,2,x),(2,3,1):}], A^(-1)=[{:((1)/(2),-4,(5)/(2)),(-(...

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  5. (A^(3))^(-1)=(A^(-1))^(3), where A is a square matrix and |A| ne 0.

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  6. (aA)^(-1)=(1)/(a)A^(-1), where a is any real number and A is a square ...

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  7. |A^(-1)| ne |A|^(-1) , where A is non-singular matrix.

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  8. If A and B are matrices of order 3 and |A|=5, |B|=3, then |3AB|=27xx5x...

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  9. If the value of a third order determinant is 12, then the value of the...

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  10. Without expanding the determinant at any stage, prove that {:|(x+1,x+2...

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  11. |adj.A|=|A|^(2), where a is a square matrix of order two.

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  12. The determinant |{:(sinA,cosA,sinA+cosB),(sinB,cosA,sinB+cosB),(sinC,c...

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  13. If the determiant |{:(x+a,p+u,l+f),(y+b,q+v,m+g),(z+c,r+w,n+h):}| spli...

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  14. Let Delta=|{:(a,p,x),(b,q,y),(c,r,z):}|=16, then Delta(1)=|{:(p+x,a+x,...

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  15. Find the maximum value of : {:|(1,1,1),(1,1+sintheta,1),(1,1,1+costh...

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  16. If A=[{:(3,4),(1,2):}], then the value of 3|A| is 6.

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  17. If |{:(2x,x+3),(2(x+1),x+1):}|=|{:(1,5),(3,3):}|, then the value of x ...

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  18. If A=({:(a,3),(3,a):}) and |A|^(3)=-125 , then a equals +2.

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  19. The value of the determinant |{:(2,3,4),(5,6,8),(6x,9x,12x):}| is

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  20. If A is a square matrix and |A|=2, then the value of |A A'| is 5.

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