Semester : SEMESTER 1
Subject : LINEAR ALGEBRA AND CALCULUS
Year : 2021
Term : JANUARY
Branch : MECHANICAL ENGINEERING
Scheme : 2019 Full Time
Course Code : MAT 101
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0000MAT101121904
PART B
Answer one full question from each module, each question carries 14 marks
Module-I
11 a) Test for consistency and solve the system of equations (7)
x+2y-z=3
3x -y + 22= 1
2 x-2 y+ 32 = 2
x -y+z=-l
b) 1 1 2 (7)
Find the eigenvalues and eigenvectorsof |-1 2 1
0 1 3
12 a) For what values of a and b do the system of equations (7)
x+y+z=6
x + 2y +3z= 10
x+2y+az=b
have 1) no solution ii) unique solution iii) more than one solution.
b) Find the matrix of transformation that diagonalize the matrix (7)
8 -6 2
4 = | -6 7 -4|. Also write the diagonal matrix.
2 -4 3
Module-II
13 a) xyz). Ou Ou Ou (7)
If If w= f| —,—,—| find the value of x—+ y—+z—.
yzx Ox “Oy ര;
0) If the local linear approximation of ೩ function 27 y, Z)= ऋ + 2212 (7)
point Pis L(x, y,z) = y+ 22 - جد find the point P.
14 a) ; 1 oz (7)
If 6८८7, x=2u+v, y=— find —.
ப் 1۷
b) Locate all relative extrema of f(x,y) = 3x* — 2xy + y* - By. (7)
Module-III
15 a) ० ० ہے (7)
Evaluate | | —dydx by reversing the order of integration.
0 x
b) Using triple integral find the volume of the solid in the first octant bounded (7)
by the coordinate planes and the plane x ~+ 21 + 2 = 6.
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