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Without expanding or evaluating show that `|[0 , b-a , c-a] , [a-b , 0 , c-b] , [a-c , b-c , 0]|=0`

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. In a triangleABC, if |[1,1,1][1+sinA,1+sinB,1+sinC],[sinA+sin^2A, sinB...

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  2. Show that : |[x, y, z ],[x^2,y^2,z^2],[x^3,y^3,z^3]|=x y z(x-y)(y-z)(z...

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  3. Without expanding or evaluating show that |[0 , b-a , c-a] , [a-b , 0...

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  4. If A is a skew-symmetric matrix of odd order n , then |A|=0

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  5. Using properties of determinants, show that |{:(x, p, q), ( p, x, q)...

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  6. If f(x)=|[a,-1 ,0],[ax,a,-1],[a x^2,a x, a]|, using properties of det...

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  7. If a , b , c are distinct real numbers and the system of equations a x...

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  8. If x , y , z are not all zero such that a x+y+z=0, x+b y+z=0, ...

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  9. Find the value of lambda for which the homogeneous system of equations...

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  10. If the system of equations x=c y+b z y=a z+c x z=b x+a y has...

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  11. A matrix A of order 3x3 has determinant 5. What is the value of |3A|?

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  12. If A is a square matrix such that |A|=2 , write the value of |AA^T|

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  13. Find the real values of lambda for which the following system of linea...

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  14. If a , b , c are non-zero real numbers and if the system of equations...

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  15. Which of the following is not correct in a given determinant of A , wh...

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  16. Let |x2xx^2x6xx6|=a x^4+b x^3+c x^2+dx+edot Then, the value of 5a+4b+3...

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  17. Let delta=|A x x^2 1 B y y^2 1 C z z^2 1|a n d1=|A B C x y z y z z xx ...

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  18. If Delta1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta2=|[q,-b, y],[-p,...

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  19. Without expanding show that: =|(cose c^2theta,cot^2theta,1),(cot^2thet...

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  20. Find the value of the determinant =|(2, 3, 4),( 5, 6, 8),( 6x,9x ,12 x...

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