Question

What is the null space of an invertible matrix?

Answer 1

`{ 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))`.