> this book is meant for the audience who can read and write proofs
It seems like the opposite is true:
"It is intended for a student who, while not yet very familiar with abstract reasoning, is willing to study more [than a] "cookbook style" calculus type course."
(from the link).
If your point is one can't learn linear algebra before learning "abstract [mathematical] reasoning"...don't think you're the main target audience of a subject as practical as linear algebra.
> Besides being a first course in linear algebra it is also supposed to be a first course introducing a student to rigorous proof, formal definitions---in short, to the style of modern theoretical (abstract) mathematics.
So I think it's fair to say that the book (ought to) assume zero knowledge of proofs, contra your parent's claim that the audience is expected to be able to read and write proofs.
It seems like the opposite is true:
"It is intended for a student who, while not yet very familiar with abstract reasoning, is willing to study more [than a] "cookbook style" calculus type course."
(from the link).
If your point is one can't learn linear algebra before learning "abstract [mathematical] reasoning"...don't think you're the main target audience of a subject as practical as linear algebra.