Is the sum of an invertible matrix with a non-invertible matrix necessarily non-invertible?
1 Answer
Mar 10, 2016
No.
Explanation:
For example:
#((1,0),(0,1)) + ((0,0),(0,0)) = ((1, 0),(0,1))#
Or a less trivial example:
#((1, 0, 1), (0, 1, 0), (0, 0, 1)) + ((0, 0, -1), (0, 0, 0), (1, 0, 0)) = ((1, 0, 0), (0, 1, 0), (1, 0, 1))#
