R3902 Pages:

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PART C
Answer any twofull questions, each carries 20 marks
7 ൭൫൪)
Find the Eigen value and Eigen vector ofthe matrix A— 0 46
: 0) 1 2(6)
21
Find the rank of the a ©
. 14 17
matrix
15
8 1
€) Solve the system of equations x —y + 7 = 0, —x y— z=0, (6)
IOy+ 252 = 90 ,20x + loy 80
8 9) Find out what type of conic section the quadratic form (8) q = 3x17 + 21x1x2 + 3+2 = 0
represents.
b)(6) Show that the matrix A= [3 0 ۳ O Lis orthogonal.
c) Show that the system [9 1 ೫3| ofequations are inconsistent. (6)
0 V3 1

2x4 6y= -11,6x+ 20y— 6z — - —3, 6y- 182 = -1

9 a) (i) Show that the vectors (1,—1,0),(1,3,_})and (5,3, —2) are linearly (8)

dependent.

(ii) Show that the quadratic form 4112 12x1x2 + 1313 = 16 is positive

definite.
b) 2 ९ 6(12)
Diagonalize the matrix 12 - 6 9
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