
Code No. R07A1BS06 Set No. 1
I B. Tech. Supplementary Examination Aug./Sep. 2008
Mathematical Methods
Time: 3 hours Max Marks: 80
Answer any FIVE Questions
All questions carry equal marks
1. (a) Solve the system 2x − y + 3z = 0,
3x + 2y + z = 0 and x − 4y + 5z = 0.
(b) Find all the solutions of the system of
equations x + 2y − z = 0, 2x + y + z = 0,
x − 4y + 5z = 0. [8 + 8]
2. Find the eigenvalues and eigenvectors of
164
04 2
063
−−
⎡⎤
⎢⎥
⎢⎥
⎢⎥
−−
⎣⎦
. [16]
3. Find the transformation that will transform
10x
2
+ 2y
2
+ 5z
2
+ 6yz − 10zx − 4xy into a sum
of squares and fi nd its reduced form. [16]
4. (a) Solve the equation x
3
+ x
2