Semester : SEMESTER 3
Subject : Linear Algebra & Complex Analysis
Year : 2019
Term : MAY
Branch : MECHANICAL ENGINEERING
Scheme : 2015 Full Time
Course Code : MA 201
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C1100 Pages: 2
2-2
f@) = 7൭ = tanz رم
E 27 4.
valuate So 5-36
Evaluate ع 1092707 where C is the circle |z| = 1
00 x?
Evaluate |
-ഠ (x24+1)(x24+4)
PART C
Answer any two full questions, each carries 20 marks
1 2 3 4
Fi ಸ 12 1 4 5
ind the rank of the matrix 15 5 7
8 1 14 17
Find the values of a and b for which the system of linear equations
x+2y+3z = 6,x+3y+5z = 9,2x+5y + az =b has (i) no solution
(ii) a unique solution (iii) infinitely many solutions
Show that the vectors[3 4 0 1], [2 -1 3 5] and [1 6 -8 -2]
are linearly independent in ೧5,
Solve the system of equations by Gauss Elimination Method:
3x + 3} + 22 = 1, > + 2) = 4, 109 + 32 = -2, 22८ - 3) - 2 = 5
Find the nature, index, rank and signature of the quadratic form
ऋ + 22 + 3x2 + 22122 - 22123 + 22223
4 2 -2
Find the Eigen values and Eigen vectors of | 2 5 0 |
-2 0 3
2 -1 1
Diagonalize the matrix ಗೆ = | -1 2 -1
1 -1 2
Define symmetric and skew symmetric matrices. Show that any real square
matrix can be written as the sum of a symmetric and a skew symmetric matrix.
What type of conic section is represented by the quadratic form
3x?+22xy+3y” = 0 by reducing it into canonical form.
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