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Consider the system of equation x+y+z=6,...

Consider the system of equation `x+y+z=6,x+2y+3z=10 ,a n dx+2y+lambdaz=mudot` then show that Statement 1: if the system has infinite number of solutions, then `mu=10.` Statement 2: The determinant `|(1 ,1, 6), (1, 2, 10),(1, 2,mu)|`= 0 for `mu=10.`

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CENGAGE PUBLICATION-DETERMINANTS-All Questions
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  2. If y=|[sinx,cosx,sinx],[cosx,-sinx,cosx],[x,1, 1]| find (dy)/(dx)dot

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  3. Consider the system of equation x+y+z=6,x+2y+3z=10 ,a n dx+2y+lambdaz=...

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  4. Consider the system linear equations in x ,y ,a n dz given by (sin3the...

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  5. If alpha,beta "and" gamma are real number without expanding at any sta...

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  6. If 3 digit numbers A28, 3B9 and 62C are divisible by a fixed constant ...

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  7. If a=costheta+isintheta,b=cos2theta-isin2theta,c=cos3theta+i sin3theta...

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  8. Prove that |[a1alpha1+b1beta1, a1alpha2+b1beta2, a1alpha3+b1beta3], [a...

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  9. If alpha,beta,gamma are the roots of p x^3+q x^2+r=0, then the value o...

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  10. Show that abs(((a-x)^2,(a-y)^2,(a-z)^2) , ((b-x)^2,(b-y)^2,(b-z)^2) ...

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  11. If |[1, x, x^2], [x, x^2, 1], [x^2, 1, x]|=3, then find the value ...

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  12. If |[x^n, x^(n+2), x^(n+3)], [y^n, y^(n+2), y^(n+3)], [z^n, z^(n+2), z...

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  13. Solve the system of the equations: a x+b y+c z=d, a^2x+b^2y+c^2z=d^2,...

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  14. If |[a,b-c,c+b],[a+c,b,c-a],[a-b,a+b,c]|=0 , then the line a x+b y+c=0...

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  15. If 2a x-2y+3z=0,x+a y+2z=0,a n d, 2x+a z=0 have a nontrivial solutio...

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

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  17. If f(x)=a+b x+c x^2 and alpha,beta,gamma are the roots of the equation...

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  18. If x ,y \ a n d \ z are not all zero and connected by the equations ...

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  19. Find lambda for which the system of equations x+y-2z=0,2x-3y+z=0,x-...

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  20. If p ,q ,r are in A.P. then value of determinant |[a^2+2^(n+1)+2p, b^2...

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