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If x , y , z are not all zero such that...

If `x , y , z` are not all zero such that `a x+y+z=0`, `x+b y+z=0`, `x+y+c z=0` then prove that `1/(1-a)+1/(1-b)+1/(1-c)=1`

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To prove that \[ \frac{1}{1-a} + \frac{1}{1-b} + \frac{1}{1-c} = 1 \] given the equations: ...
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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. If f(x)=|[a,-1 ,0],[ax,a,-1],[a x^2,a x, a]|, using properties of det...

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

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

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

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

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

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

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

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

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  11. 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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  12. 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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  13. If Delta1=|[a, b, c],[ x, y, z],[ p, q, r]| and Delta2=|[q,-b, y],[-p,...

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

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

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  16. Without expanding evaluate the determinant |[41,1,5],[79,7,9],[29,5,3]...

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  17. Show that |1a bc1b c+a1c a+b|=0

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  18. Without expanding evaluate the determinant |[(a^x+a^(-x))^2,(a^x-a^(-x...

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  19. If D1=|[1, 1, 1],[x^2,y^2,z^2],[x, y, z]| and D2=|[1, 1, 1],[yz, zx,xy...

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  20. Without expanding show that |[b^2c^2,b c, b+c],[c^2a^2,c a ,c+a ],[a^2...

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