>>12799898Except that
1. Your equations don't have to equate to the zero vector, so "solution to an equation" is vague as fuck and could refer to an affine target set instead.
2. That definition is utterly useless for homomorphisms between other algebras such as groups or rings. The kernel in general is defined as the pre-image of the trivial subspace, which is the set containing the zero vector for linear spaces.
Lurk moar, faggot.