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

Let `Delta=|{:(a,p,x),(b,q,y),(c,r,z):}|=16`, then `Delta_(1)=|{:(p+x,a+x,a+p),(q+y,b+y,b+q),(r+z,c+z,c+r):}|=32`

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If a, b, c are three given non-coplanar vectors and any arbitratry vector r is in space, where Delta_1=|[r*a, b*a, c*a], [r*b, b*b, c*b], [r*c, b*c, c*c]| : Delta_2=|[a*a, r*a, c*a], [a*b, r*b, c*b], [a*c, r*c, c*c]| Delta_3=|[a*a, b*a, r*a], [a*b, b*b, r*b], [a*c, b*c, r*c]|, Delta_4=|[a*a, b*a, c*a], [a*b, b*b, c*b], [a*c, c*c, c*c]| Q. The vector r is expressible in the form

ACCURATE PUBLICATION-DETERMINANTS-Type-III (True or False questions)
  1. (aA)^(-1)=(1)/(a)A^(-1), where a is any real number and A is a square ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. A matrix A of order 3xx3 is such that |A|=4. Then the value of |2A| is...

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  17. The value of determinant |{:(2,a,abc),(2,b,abc),(2,c,abc):}| is 0.

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  18. The value of determinant |{:(11,12,13),(12,13,14),(13,14,15):}| is 1.

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  19. If A is a square matrix of order 3 and |3A| = k|A|, then write the val...

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  20. prove (A^(-1))'=(A')^(-1)

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