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FOURTH SEMESTER (CBCSS—UG) DEGREE EXAMINATION
APRIL 2023

Mathematics
MTS 4B 04—LINEAR ALGEBRA
(2019 Admission onwards)
Time : Two Hours and a Half Maximum : 80 Marks
Section A (Short Answer type Question)

Each question carries 2 marks.
All questions can be attended.
Overall ceiling 25.

1. Give an example of a system of linear equation with the following properties :
(i) Unique solution ; and
Gi) Nosolution.

2. For any 2 x 2 matrices, A and B, prove that
trace (A + B) = trace (A) + trace (B)
3. Define all subspaces of the vector space R® over R.

4. Define linear combination of vectors in a vector space. Write (2, 3) as the linear combination of

(1,0) and (0,1).

5. Define basis of a vector space. Write a basis of P,, where P,, is the polynomials of degree less than

or equal to n.
6. Consider the basis B ={uw,, u,} and B’ = {wu}, us} of R®, where w, =(1, 0), ‏وك‎ = (0,1), uj, =(1, 1) and

us =(2,1). Find the transformation matrix from B’ > B.

7. Let W={(x,) eR? :x+y=0}. Find the dimension of W.

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