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NSA192001 Pages:4

PART B
Answer one full question from each module, each question carries 14 marks

Module-I
Solve the system of equations by Gauss elimination method.

x+2y+3z=1
2x +3y+2z=2
3x +3y+4z=1

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Find the eigenvalues and eigenvectors 0
4 2 -2
2 5 O
2 0 3
Find the values of A and ൧ for which the system of equations
2x + 3y + 52 = 9
Tx + 3y -22 = 8
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‎has (i) no solution (ii) a unique solution and (iii) infinite solution
Find the matrix of transformation that diagonalize the matrix
1 -3 3
A=|3 -5 3) . Also write the diagonal matrix.
6 -6 4
Module-II
Let f be a differentiable function of three variables and suppose that
Ow Ow Ow
w= f(x-y, y—2Z,z—x) show that —+—+— =
2-2.) ) ox Oy &

Locate all relative extrema of f(x,y) = 4xy — y* — 24

Find the local linear approximation 1, to the function f(x, y) = ಹಾ + y?
at the point P(3,4).Compare the error in approximating f by L at the point

Q(3.04,3.98) with the distance PQ.

The radius and height of a right circular cone are measured with errors of at
most 1% and 4%, respectively. Use differentials to approximate the
maximum percentage error in the calculated volume.

Module-III

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