The linear combination picture is extremely misleading: the gray dots show the linear combinations where the coefficients are integers, but we are in the vector space R^2! This could have been a great opportunity to teach that any vector in R^2 could become a linear combination of these two vectors, thus it could become a new coordinate system.

Even though this is probably introduced in a later chapter, a curious reader will be able to question why the gray dots are form with integer coefficients and leave them with a wrong impression.