Jaypee Institute of Information Technology (JIIT) 2008 M.Tech Computer Science Supplimentary - Linear Algebra for ICWA - Question Paper
Jaypee University orinformalion Technology Waknaghat Test 3 May 2008 M. Tech. IV Scm. (IMCA)
Subject Code: MA--lime: I Hr. 30 min.
Subject Name: Linear Algebra M.M.: 30
Show that the vectors a, =(1.0,-l). cr, =(1.2.1). a. = (0,-3.2) form a basis for R\ Express each of the standard basis vcctors as a linear combination of
(S)
<5)
(5)
Every n-dimensiooal vector space V(F) is isomorphic to V(F). Find the dual basis of the basis set 5 = {(l.-l,3),(0tl,-lM0.3.-2)]
forVR).
Is the matrix
(5)
similar over the field R to a diagonal matrix? Is A similar over the field C to a diagonal matrix?
a) If a is a characteristic vcctor ofT, then a cannot correspond to more than one characteristic values of T. (2.5)
b) Let T be a linear operator on a finite dimensional vector spacc V and let c be a characteristic value of T. Show (hat the characteristic space of c i.e.. Wt is invariant under T. (2.5) Apply Ihc Gram-Schmidl process to the vcctors
"(l.O, l),/7j * (l, 0, -1}/?, ={0,3,4)L to obtain an orthonomtal basis for Vj(R) with the standard inner product. (S)
6.
|
Attachment: |
| Earning: Approval pending. |
