sample question papers

 

2105 – DMI COLLEGE OF ENGINEERING

Internal Assessment Test - II(2018-2019 - ODD)

2018/ III

MA 8352&LINEAR ALGEBRA & PDE

Date :xx-xx-xxxx& Time:10.30 To 12.30 P.M                                 Max. : 60 Marks

Note:

·          Draw neat sketch with pencil (if necessary)

·          Use chart or tables (if necessary)

·          Answer all questions

Part – A (6*2=12)

1.      Solve p+q=pq

2.      Find the complete intergral of pq=xy

3.      Let W={(a_1,a_2,a₃)/a₁=a₃+2} prove that it is not a subspace of V.

4.      State and prove Cancellation Law for Vector addition.

5.      If V=P(x) is a vector space over F. let S={1,x,1+x²} check whether S is linearly independent or not.

6.      Define Null space N(T).

Part – B (4*12=48)

7.      i) W₁ and W₂ be subspaces of V. prove that W₁UW₂ is asubspaces of V if and only if W₁ contained are equal toW_{2 .}ii) Let W be a subspaces of a finite dimensional vector space V. Then W is finite dimensional and dim(W)≤dim(V) . Moreover if dim(W)=dim(V)=W.

8.      i)Write a vector v=(1,-2,5) as a linera combination of the vectors e₁=(1,1,1) , e₂=(1,2,3) , e₃=(2,-1,1). ii) State and prove direct sum theorem.

9.      i)State and prove dimension theorem. ii) Let V and W be vector spaces, and let T:V→W be linear. Then T is one –to-one iff N(T)={O} .

10.  i)Solve (D²+2DD’+D’²-2D-2D’)z=sin(x+2y) .

ii)Solve p³+q³=27z .