IIT Madras MS DSAI Written Test 2024

Question

Given, that the eigen values of a 2 x 2 matrix are -1,1 and its singular values are 1,0. What is the rank of the matrix?
a) rank is 0
b) rank is 1
c) Such a matrix can't exist
d) rank is 2

Answer 1

$\Rightarrow $  Rank of  a matrix  is Non Zero Singular Values .

Proof- http://faculty.washington.edu/trogdon/105A/html/Lecture25.html

$\Rightarrow $ But here non zero eigen values are also given which means Full rank must be there .

From both of these we can Conclude that  No such Matrix exist. So option $C$ should be Ans.