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Find the real values of k for which the ...

Find the real values of k for which the following system of linear equations has non-trivial solutions:
x-ky+z=0,kx+3y-kz=0,3x+y-z=0

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The correct Answer is:
2 or, -3
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Show that the following system of equations has no solution : x+2y+3z=1,2x+3y+5z=1,3x+4y+7z=1

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For what values of k , the following system of equations possesses a nontrival solution over the set of rationals: x+k y+3z=0,3x+k y-2z=0,2x+3y-4z=0. Also find the solution for this value of kdot

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CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2C
  1. Find the real values of lambda for which the following system of linea...

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  2. Find the real values of k for which the following system of linear eq...

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  3. Find the real values of k for which the following system of linear equ...

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  4. Find the real values of a for which the system of equations a^3x+(a+...

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  5. |{:(1,2,3),(4,5,6),(3,2,2):}|

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  6. |{:(2,3,4),(5,6,1),(3,2,3):}|

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  7. Using determinant : find the area of the triangle formed by joinin...

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  8. Using determinant : Show that the points (a,b+c),(b,c+a) and (c,a+b...

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  9. Using determinant : find the area of the triangle whose vertices ar...

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  10. Using determinant : show that the area of the triangle whose vertice...

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  11. Using determinant : Find the value of t for which the area of the t...

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  12. Using determinant : show that the points (a+1,a) ,(a,a+1) and [(a+1)...

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  13. Using determinant : show that the area of the triangle with vertices...

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  14. Eliminating x and y from the following equations, obtain the value of ...

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  15. Eliminate x,y and z from the following equations: (x)/(y+z)=a,y/(z+x...

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  16. Show that the following system of equations has no solution : x+2y...

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  17. Show that the following system of equations has infinite number of s...

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  18. a-b+c=6,4a+2b+c=11,9a-3b+c=6

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  19. 2x-y=4,x-2y+1=0

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  20. x+y-z=-3,2x+3y+z=2,8y+3z=1

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