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For what values of k , the following s...

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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CENGAGE ENGLISH-DETERMINANTS-All Questions
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  2. If p ,q ,r are in A.P. then value of determinant |[a^2+2^(n+1)+2p, b^2...

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  3. For what values of k , the following system of equations possesses a...

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  4. Let a ,b , c in R such that no two of them are equal and satisfy |(2a...

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  5. Solve for x by Cramers rule x+y+z=6, x-y+z=2 3x+2y-4z=-5

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  6. The value of the determinant |(k a, k^2+a^2, 1),(k b, k^2+b^2, 1),(k c...

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  7. Find the value of a \ a n d \ b if the system of equation a^2x-b y=a...

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  8. If (x1-x2)^2+(y1-y2)^2=a^2, (x2-x3)^2+(y2-y3)^2=b^2, (x3-x1)^2+(y3-y1...

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  9. f(x)=|[cosx,x,1],[2sinx,x^2,2x],[tanx,x,1]| . Then value of lim(x->0)(...

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  10. If a system of three linear equations x+4a y+a=0,x+3b y+b=0, and x+2c...

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  11. Let alpha be a repeated root of a quadratic equation f(x)=0 and A(x...

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  12. If |[a^2+lambda^2,ab+clambda,ca-blambda],[ab-clambda,b^2+lambda^2,bc+a...

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  13. Value of |{:(1+x(1),,1+x(1)x,,1+x(1)x^(2)),(1+x(2),,1+x(2)x,,1+x(2)x^(...

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  14. If f(x)=|(a1+x, b1+x, c1+x), (a2+x, b2+x, c2+x),(a3+x, b3+x, c3+x)|, s...

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  15. The value of determinant |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b...

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  16. Prove that the value of each the following determinants is zero: |a...

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  17. If l1^2+m1^2+n1^2=1 etc., and l1 l2+m1 m2+n1 n2 = 0, etc. and Delta...

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  18. The value of determinant |[ ^n C(r-1), ^n Cr, (r+1)^(n+2)C(r+1)],[ ^n...

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  19. Let |(x,2,x),(x^2,x,6),(x,x,6)|=A x^4+B x^3+C x^2+D x+Edot Then the va...

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  20. If the determinant |b-cc-a a-bb^(prime)-c ' c^(prime)-a ' a^(prime)-b ...

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