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Solve the following system of equations ...

Solve the following system of equations by using determinants: `x+y+z=1`, `a x+b y+c z=k`, `a^2x+b^2y+c^2z=k^2`.

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RD SHARMA ENGLISH-DETERMINANTS-All Questions
  1. Using determinants, show that the following system of linear equation ...

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  2. By using determinants, solve the following system of equations: x+y+z=...

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  3. Solve the following system of equations by using determinants: x+y+z=1...

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  4. Using Cramers rule, solve the following system of linear equations: (...

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  5. If |[a, p, x],[ b, q, y], [c, r, z]|=16 , then the value of |[p+x, a+x...

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  6. The value of |1 1 1^n C1^(n+2)C1^(n+4)C1^n C2^(n+2)C2^(n+4)C2| is

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  7. Solve the following system of homogeneous equations: x+y-z=0 x-2y+...

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  8. For what values of aa n db , the system of equations 2x+a y+6z=8 x+2y...

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  9. If x , y , z are different from zero and |[1+x,1, 1],[1 , 1+y ,1],[ 1...

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  10. Evaluate the following determinants: |x-7x5x+1| (ii) |costheta-sin...

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  11. If [] denotes the greatest integer less than or equal to the real numb...

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  12. Let |(3,y), (x,1)|=|(3,2), (4,1)| . Find possible values of x and y ar...

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  13. If |[x-2,-3],[3x,2x]|=3 find the value of x

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  14. Let A=|[1,sintheta,1],[-sintheta,1,sintheta],[-1,-sintheta,1]|, where ...

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  15. Find the minors and cofactors of elements of the matrix A=[a(i j)]=[[1...

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  16. Evaluate =|[-1, 6,-2],[ 2, 1, 1],[ 4, 1,-3]| by two methods

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  17. If A=[1 3 2 1] , find the determinant of the matrix A^2-2Adot

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  18. Determine the values of x for which the matrix A=[(x+1,-3 ,4),(-5,x+2,...

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  19. The value of the determinant |[x, x+y, x+2y], [x+2y, x,x+y],[x+y, x+2y...

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  20. The number of distinct real roots of |(cosecx,secx,secx),(secx, cosecx...

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