C192001 Pages: 2

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०) മു 1 ⋅ ⋅ ⋅
valuate So 0212 dxusing contour integration. (8)
PART C
Answer any two full questions, each carries 20 marks
a) Solve the system of equations using Gauss Elimination method:
yt+z—2w=0, 2x - 3y - 32 + 6w ಎ 2, 4x + ) 1 2 - 210 = 4 (8)

b) 1 அ இய
Ifthe matrix |2 1 —1 2 | is of rank 2, find the values of a, ¢.
6-2 a മ (6)
c) Check whether the vectors [1, 2, 1], [2, 1, 4], [4, 5, 6], [1, 8, -3]
are linearly dependent in ۰ (6)
a) 61454, 2
Diagonalise the symmetric matrix]—2 3 -1
[അന്ന (8)
b) =A 4൧ ٠٦
If one eigen values of the matrix A = | 2 1 - 615 5, find the other
9 2 0

eigen values without finding the characteristic equation. What are the eigen (6)
values of A? and 4 7.

c) Reduce the quadratic form q = 3x* +5y? + 322 - 292 + 22% — 2xy to the

canonical form. Examine the definiteness. (6)
a) ७0 அ!
Find a matrix B which transform A=|1 2 1 Jin to the diagonal form.
१ 2 ആ ^)

0) Find a basis and dimension for the row space, column space and null space for

1 2 0 2 5
.. 4 (2 5 1 -1 -8
the matrix A = ۴ 3 4 1 )10(
3 6 0 -7 2
HOR ಶೇತೇ

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