What is the use of Null Space?

Dear fellow mathematician,

at first, it might appear that it is not really as useful. But the opposite is true, you are going to use it to find eigenvectors which are of huge importance in linear algebra. They are used for diagonalising matrices and for Singular Value Decomposition which is of vital importance. (it’s a numerically stable way of taking powers of matrices - solving differential equations and many other things - i.e. finding n-th term of a sequence from a reccurent formula, which can be used for various)

These are the applications that I’m familiar with, I’m sure that someone will provide more.

Have a nice Sunday!