Inverse, Column space and null space

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Inverse

We can use Inverse transformation to resolve the function.

Column space

The column sapce is the span of the columns of the matrix.

And the column space represents the rank of the matrix.

When a 3-D matrix has rank 3, we can call it full rank.

Null space

For a full rank matrix only origin can be squished into origin.
But for a matrices aren’t full rank, which squish to a smaller dimension, you can have a whole bunch of vectors that land on zero.

For a 2-D matrix, if its rank is 1, it squish all the vectors on a line to the origin.

For a 3-D matrix, if its rank is 1, it squish all the vectors on a plane to the origin, if its rank is 2, it squish all the vectors on a line to the origin.

Reference
https://www.3blue1brown.com/topics/linear-algebra