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Show that the following system is incons...

Show that the following system is inconsistent.
(a-b)x+(b-c)y+(c-a)z=0
(b-c)x+(c-a)y+(a-b)z=0
(c-a)x+(a-b)y+(b-c)z=1

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The correct Answer is:
` :. ` The system has no solution and system is inconsistent .
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ARIHANT PRAKASHAN-SIMILAR TEST 3 -SECTION B
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  2. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

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  3. Show that the following system is inconsistent. (a-b)x+(b-c)y+(c-a)z...

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  4. If A=[{:(3,-2),(4,-2):}], then find k such that A^(2)=kA-2I .

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  5. On a multiple choice examination with three possible options for each ...

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  6. An instructor has a question bank consisting of 300 easy true/false qu...

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  7. If y = log (x+sqrt(1+x^(2))) , then find y(2)(0).

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  8. Differentiate the following function w.r.t. x, (logx)^(x)+x^(logx).

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  9. Find the equation of normal to the curve y = e^(sin x) " at "x = pi...

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  10. Find the approximate value of f(2.01), where f(x) = 4x^(2) + 5x+2

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  11. Discuss the continuity of the function f(x) at x=1/2 , when f(x) is de...

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  12. Integrate int cot^(-1) x dx.

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  13. Integrate int sqrt (7x-10 -x^(2)) dx

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  14. Evaluate int(0)^(pi) |cos x |dx.

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  15. Find the area bounded by y = |x-1| and y=1 .

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  16. Solve (dy)/(dx) +(sec x) y = tan x.

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  17. Find the area of the parallelogram whose diagonals are the vectors 3ha...

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  18. Find the angle between the lines whose direction cosines are given by ...

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  19. Prove that the point (1,2,3),(-1,1,0),(2, 1, 3) and (1, 1, 2) are copl...

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  20. Find the points of intersection of the line (x-1)/1=(y+2)/ 3 =(z-1)/(...

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