What is the null space of an invertible matrix?

1 Answer
Jul 17, 2017

Answer:

#{ underline(0) }#

Explanation:

If a matrix #M# is invertible, then the only point which it maps to #underline(0)# by multiplication is #underline(0)#.

For example, if #M# is an invertible #3xx3# matrix with inverse #M^(-1)# and:

#M((x),(y),(z)) = ((0),(0),(0))#

then:

#((x),(y),(z)) = M^(-1)M((x),(y),(z)) = M^(-1)((0),(0),(0)) = ((0),(0),(0))#

So the null space of #M# is the #0#-dimensional subspace containing the single point #((0),(0),(0))#.