30 points
>
Time management is very much important in IIT JAM. The eduncle test series for IIT JAM Mathematical Statistics helped me a lot in this portion. I am very thankful to the test series I bought from eduncle.
Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
- IIT JAM
- Mathematics (MA)
Algebric multiplicity
algebric multiplicity how is this?? lambda ^2 =0 but a.m of 0 is 1
1 Answer(s)
Answer Now
- 0 Likes
- 2 Comments
- 0 Shares
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
Sign Up to Download FREE Study Material Worth Rs. 500/-
Ujjawal vishal
Your calculation seems wrong. It is not lambda^2 = 0 See, Characteristic equation is |A- xI| =0. => (2-x)(2-x) - 4 =0 => x^2 - 4x =0 => x(x-4)=0 => x =0, 4 So, AM of 0 =1 AM of 4 =1 and we know that, G.M ≤A.M That means here G.M. for both the eigen values is ≤ 1 i.e 0 or 1. To find G.M of eigen value 'x' find the nullity of matrix (A-xI). For , x =0 we have to check nullity A-0.I = A clearly ,rank of A is 1 then use rank nullity theorem. Similarly, for x = 4 ,we have to check nullity of matrix (A -4I)