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01MAT101121903-B

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

Module-I
Using Gauss elimination method find the solution of the system

xty—z=9,8y + 62 = —6,—2x+ ‏برك‎ - 62 = 40
Find the matrix of transformation that diagonalize the matrix
3 i ‏گے‎
‎-2 1 2

0 1 2

. Also, find the diagonal matrix.

Find the value of ۸ and ‏بر‎ for which the system of equations
2x+3y+5z=9 7%43)- 22 = 8 2x+3y+ Az= ‏پر‎
‎has (a) no solution (b) unique solution (c) more than one solution
न 2 പടി
Find the eigen values and eigen vectors for the matrix | 2 1 ஈட்‌
-1 —2 0
Module-II

If ‏در‎ + 92 +z? + y? + ८2 , 2೫0060, ‏صما 2 ,56100 پر‎ ©,

Find the local linear approximation L of f(x, y,z)=xyz at the point
P(1,2,3). Compute the error in approximation f by L at the point
Q(1.001,2.002,3.003).

Locate all relative extrema of f(x, y) = 3 y?(12 —x-y)

Let f be a differentiable function of three variables and suppose that

w= f(x ൦707൦242 —x), show that Ow | Ow , OW 0
Ox Oy 02
Module-III

Find the area bounded by the x — axis, y= 2x, x+y = 1.
1 2-x
Change the order of integration and hence evaluate ॥ [dydx
0 x

Find the volume bounded by the cylinder 2 + 32 =9 and the planes

y+z=3and z=0

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