What do the numbers in a vector describe?
Translate between an arrow and a list of coordinates. Each representation makes a different aspect of the same object easier to inspect.
Read on through a shared source
What is the same in a diagram and a column calculation? →Switch between geometric motion and coordinate arithmetic to see one linear operation from two angles. Strang’s column combination is a worked example; neither representation is best for every task.Does getting the answer mean understanding the concept? →Concept questions in physics and geometric intuition in linear algebra reveal gaps that procedural success can hide. Neither approach rules out calculation practice.What does multiplying a vector mean? →Scaling one vector and combining two vectors are different operations. Check the operands and the type of result before interpreting the notation.
Compare the passages
the geometric understanding is what lets you judge what tools to usea language to describe space and the manipulation of space using numbers that can be crunched and run through a computer.