A NSA192001

Reg No.:

FIRST SEMESTER B.TECH DEGREE EXAMINATION(2019 SCHEME), DECEMBER 2019

Course Code: MAT101
Course Name: LINEAR ALGEBRA AND CALCULUS
(2019-Scheme)

Max. Marks: 100 Duration: 3 Hours
PARTA
Answer all questions, each carries 3 marks.
1 1 1 (3)
1 Determine the rank of the matrixA = |1 2 3
1 2 5.
3 -1 1 (3)
If 2 is an eigen value of |-1 5 -1| without using its characteristic
2 1 -1 3

equation, find the other eigen values.

3 If f(x,y) = +€ +5y find the slope of f(x,y) in the x-direction at (4,0). (3)
‏ج62‎ 62

4 Show that, + aye =0, where z= e*siny + 67 cosx GB)
x yo

Find the mass of the square lamina with vertices (0,0) (1,0) (1,1) and (0,1) and

5 2 (3)
density function x* ‏بر‎
‎0000 -(*2 5 2)
6 Evaluate | fe ¬ /dxdyby changing 10 polar coordinates. (3)
00
00
7 Test the convergence of the series 3)
8 (किया
2 1
8 Check the convergence 08 2 ——— (3)
k/2
k=l k
7
9 Find the Taylors series for f(x) -008% about x = 3 up to third degree terms. (3)
10 Find the Fourier half range sine series of f(x) ‏“مع‎ in0Page 1 of 4