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# KTU B.TECH S3 MODEL QUESTIONS FOR COMPLEX ANALYSIS AND LINEAR ALGEBRA

KTU B.Tech s3 Model questions for Complex analysis and linear Algebra

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KTU B.Tech s3 Model questions for Complex analysis and linear Algebra

MODEL QUESTION PAPER  II by ktubtechquestions.com

THIRD SEMESTER B.TECH  DEGREE EXAMINATION  DECEMBER 2016

MA201 LINEAR ALGEBRA AND COMPLEX ANALYSIS

Time: 3 Hrs                                                                                                Marks: 100

PART A

( Answer Any two  Questions Each carries 15 marks)

1 a) If f (z) is an analytic function with constant modulus , then prove that f (z) is a constant.

b). If w=Φ+iΨ represents the complex potential of an electric field and     determine the function Φ .

2

3   a. Find the bilinear transformation which maps the point -1, i, 1 of the z-plane  on to the points 1,i,-1  Of  the w-plane respectively

b. Show that under the transformation

, the real axis in the z-plane is mapped into the  circle │w│=1.

PART B

( Answer any TWO, Each carries 15 Marks )

5.

6.                        a.
b.

PART C

( Answer All Questions Each Carries 20 Marks )

7  a. Express v=(2,7,-4) in R3 as a linear combination of the u1=(1,2,0), u2=(1,3,2)  and u3=(0,1,3)  (10 mark)

b.Diagonalize the matrix (10 mark)

8 a. Find the rank and then find the basis for the row space and column space
(15 mark)

b. Are the following sets of vectors linearly independent?

[4  -1   3], [ 0   8    1],  [ 1   3   -5],[2   6   1]              (5 mark)

9 a. Solve the linear system by Gauss elimination method. (10 mark)

b. Find Eigen values and Eigenvectors of the following Matrix (10 mark)

x

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