367339

4
Section C (Essay Type Question)
Answer any two questions.
Each question carries 10 marks.
1 2 3 2 _
24. (a) Let A= ,B= , verify that (AB) ജക,
1 3 2 2
(b) Define the followings with examples :
(i) Diagonal matrices ;
(ii) Lower triangular matrices ;
(iii) Upper triangular matrices ;
(iv) Symmetric matrices ; and
(v) Singular matrices.
25. Let v, ={1,2,1},v, ={2, 9, 0} and v, = {3,3, 4}.
(a) Show that {vj, v2,v3} isa basis പ്‌ 15.
(b) Find the co-ordinate vector of v=(5,—1,9) relative to the basis {v1, vg, v3}.
26. Consider the following linear system :
-1 3 22 1
1 2 -3||श्| = |-9.|
2 1 -1| | »%3 -3
(a) Show that the above system is consistent.
(b) Solve the above system of linear equations.
27. (a) Define similar matrices.
(b) Show that the following matrix is not diagonazible :
100
1 2 O|.
-3 5 2
(2x 10

367339

C 41231

= 20 marks)