Question

What is Kernel and Range of a linear transformation?

Answer 1

The kernel K of a linear transformation A, is the subset of the vector space your linear transformation acts on that is sent to 0.

Answer 2

The range of a linear transformation is the subset of a vector space that is mapped to.

Answer 3

so basically, Kernel is the same as null space and Range is the span of column space

Answer 4

Kernel and null space are the exact same thing (kernel can be applied to other mathematical things though).

As for range and span of column space, those would also be the same thing, with range being more easily applicable to other mathematical areas.