Q.no. Module 3 Marks

4
Examine whether the set A ={(x,y,z)/2x-y+3z=0} Is a subspace of 83 .
Answer b orc

b 1 3 1 5

Reduced The Matrix 8-2 6 1 to echelon form and every solution to AX=0
1 3 2
Find The Linear Transformation 7: R?—— 82 such that T(1,3)=(5,-4), 8
T(-1,1)=(-1.0)Also find that T(2,2)
Q.no. Module 4 Marks
48 If 8 1185 Eigen value 1,2,3 and C has an Eigen value 4,5,6 and 0 has an Eigen 4
value 7,8,9 what are the Eigen values of the 6 by 6 matrix A= ۳ 5
Answer b orc

b 7 -1 3 5

Diagonalize the Matrix A ~ 1 1 and hence find A?
2 4 8

c Find the orthonormal Basis of R? from the given Basis B 5

={(1,1,1),(0,1,1),(0,0.1)}
Q.no. Module 5 Marks
58 ಲ್ಯ ⋅ ⋅ 5

Find the solution of the PDE wu, + uy = 0 using method of separation of

variables

Answer b orc

Classify the Following PDE and reduce to the canonical from
4८८५८ + 5tyy +Uyy + 14८ + 1८) = 2

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