• Want FREE Counselling for Exam Preparation?
###### Call Us
800-355-2211

Speak With a Friendly Mentor. ###### Deepak Patra posted an Question
January 04, 2022 • 17:58 pm 30 points
• IIT JAM
• Mathematics (MA)

# 5. let m,(k) denote the space of all nxn matrices with entries from afield k. fix a non-singular matrix a= (4) e m,(k) and map consider the linear t:m,(k) -m,(k

5. Let M,(K) denote the space of all nxn matrices with entries from afield K. Fix a non-singular matrix A= (4) e M,(K) and map consider the linear T:M,(K) -M,(K) given by: T(X) = AX. Then (a.) Trace (T)=n2iAu Aij b.) Trace (T)=Zi2ji A .(c.) Rank of T is n (d.) T is non-singular

• 0 Likes
• 0 Shares
• ##### Anonymous User

D check attachment

sir c can also be the ans ... as T is non singular dimension of A is n²

if u take identity matrix then T=I rank of T ≠n²

understand

### Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

• Updated Syllabus, Paper Pattern & Full Exam Details
• Sample Theory of Most Important Topic
• Model Test Paper with Detailed Solutions
• Last 5 Years Question Papers & Answers