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5102

Evaluate |

26

A7046

dz over the circle |z|=2 using Cauchy’s Residue theorem.

PART C

Answer any two full questions, each carries 20 marks.

Solve by Gauss-Elimination method x + y + 2 = 6, ++ 2y- 32 = -4, -x-4y+9z =18.

Find the values of ‘a’ and ‘b’ for which the system of equations x + y + 2z 52,

2x-y+3z=10,5x-y+az=b has:

(i) no solution (ii) unique solution (iii) infinite number of solutions.

Verify whether the vectors (1,2,1,2), (3,1,-2,1),(4,-3,-1,3) and (2,4,2,4) are linearly

independent in R*.

Write down the matrix associated with the quadratic form 8x 17+7x27+3x37-12x1x2

-8x2x3+4x3x1. By finding eigen values, determine nature of the quadratic form.

Diagonalise the matrix A =

Find the eigen vectors of A =

1 -2 0
-2 0 2
0 2 “ட்‌
If A is a symmetric matrix, verify whether AA? and A'A are symmetric?
3 0 0
5 4 0
3 6 1

Find the null space of AX=0 if A=

Verify whether A = |

What can you say about determinant of an orthogonal matrix? Prove or disprove the

result.

1
0
0

0
cos@
sin@

1 1 0 2
-2 -2 1 -5
1 1 -1 3
4 4 -1 9
0
—sin 1 is orthogonal.
cos 0

بد بد ‎oR‏

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