Hello sir, I am Abhijeet. I am from Kannur. I want you to help me by providing me with the 3rd Semester B.Tech Mechanical Engineering, Engineering Mathematics question paper of Kannur University. Can you help me?

As you have asked for the 3rd Semester B.Tech Mechanical Engineering, Engineering Mathematics question paper of Kannur University, I am providing you with it, check below for the details

I. a) Show that the vectors (1, 2, 3), (1, 0, 1) and (0, 1, 0) are linearly independent.

b) If V be the vector space of all functions from IR to IR and w = {f : f (5) = O} then show that w is a subspace of V.

c) Define the rank of a matrix and show that rank of A = rank of AT (AT is the transpose of A).

Show that A 2 3 IS a zero of f (t) = t2 -4t -5

Show that polar form of Cauchy-Riemann equations are
au 18v 8v -18u
5ar=r 00' ar -r 00'

Show that if f (2) = u + iv is analytiC then u is harmonic.

A set of vectors {v1, v2, ... v} is a basis of a vector space V iff each vector nin V is uniquely expressible as a linear combination of v1, v2, ... vn

Find the basis and the dimension of the subspace wof 1R4 generated by (1, -2,5, -3), (2, 3, 1, -4) and (3, 8, -3, -5).

Show that the set U of all linear combinations of n arbitrary vectors v1, v2, ... vn of a vector space V is a subspace of V and each vectors v1, v2, .. , vn is in V.




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