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If a , b , c are distinct, then the valu...

If `a , b , c` are distinct, then the value of `x` satisfying `|(0,x^2-a, x^3-b),( x^2+a,0,x^2+c), (x^4+b, x-c,0)|=0i s`
c (b) a (c) b (d) 0

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To solve the problem, we need to evaluate the determinant given by: \[ \Delta = \begin{vmatrix} 0 & x^2 - a & x^3 - b \\ x^2 + a & 0 & x^2 + c \\ x^4 + b & x - c & 0 \end{vmatrix} ...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. If Ar=|[1,r,2^r],[2,n,n^2],[n,(n(n+1))/2, 2^(n+1)]|, the value of sum(...

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  2. If the determinant |[a,b,2aalpha+3b],[b,c,2balpha+3c],[2aalpha+3b,2bal...

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  3. If a , b , c are distinct, then the value of x satisfying |(0,x^2-a, x...

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  4. Using the factor theorem it is found that a+b , b+c and c+a are thr...

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  5. Let |(x^2+3x,x-1,x+3),(x+1,-2x x-4),(x-3,x+4 ,3x)|=a x^4+b x^3+c x^2+e...

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  6. If Dk=|[1,n,n],[2k,n^2+n+2,n^2+n],[2k-1,n^2,n^2+n+2]| and sum(k=1)^...

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  7. If Delta1=|(1, 1, 1),(a, b, c),( a^2,b^2,c^2)|,Delta2=|(1,bc, a),(1,ca...

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  8. The value of the determinant |(a^2,a,1),(cosn x,cos(n+1)x,cos(n+2)x),(...

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  9. Evaluate: (i) |(5 ,4),(-2, 3)| (ii) |(sintheta,costheta),(-costheta,s...

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  10. Evaluate: (i) |(x^2+x y+y^2,x+y ),(x^2-x y+y^2,x-y)| (ii) |(1,(log)b ...

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  11. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]| by expanding it along th...

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  12. Evaluate the determinant D=|2 3-2 1 2 3-2 1-3| by expanding it alon...

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  13. Evaluate D =|[2, 3,-2],[ 1, 2, 3],[-2, 1,-3]| by using Sarrus diagram.

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  14. Evaluate =|-1 6-2 2 1 1 4 1-3| by two methods.

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  15. For what value of x the matrix A=[[1,-2,3],[1,2,1],[x,2,-3]] is singul...

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  16. Determine the values of x for which the matrix A=[x+1-3 4-5x+2 2 4 ...

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

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  18. If A=[1 2 4 2] , then show that |2A|=4|A| .

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  19. If |x-2-3 3x2x|=3 , find the values of xdot

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  20. Let |[3,y],[x,1]|=|[3,2],[4,1]| Find possible values of x and y if x,y...

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