10.

11.

12,

13.

14.

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2 C 41231
Give an example of an infinite dimensional vector space.

Define rank and nullity of a matrix.

7
Find the image of x = (1,1) under the rotation of टर about the origin.

Define eigen values and eigen vectors of a matrix.

= 0 0
2
-1 9/8 0.
Find the egien values of
1
5 ௮ ಎಮ

12.15 the eigen values of a matrix A, show that A” is the eigen values of A”

Show that (1,1) and (1, -1) are orthogonal vectors with respective the Euclidian inner product.

Let W be the subspace spanned by the orhonornal vector v, = (0, 1, 0). Find the orthogonal projection
of w= 0 1, 1) on W.

(Ceiling 25 marks)
Section B (Paragraph/Problem Type Questions)

Each question carries 5 marks.
All questions can be attended.
Overall Ceiling 35.

Solve the following linear system by Gauss-Elimination method,

8 = 28 + وند + إند
‎ध] - 29 + 328 = 1‏ -
.10 و4 + ود7 >- د3
‎Prove that, if A and B are invertible matrices of same size, then AB is invertible‏

ബര്‍ (൧8) "14,

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