Given vectors and show that every vector in is of the form for some . Express and in terms of and .

*Proof.* (**Note:** I’m doing this without any real linear algebra since we don’t get to that until Volume 2. If you do know linear algebra then you would show the two vectors and are linearly independent and you’d be done.) Since

we have

This implies

Therefore,

This also shows that any vector in can be obtained as since given we compute and by the formulas above

There is an error on the first line

Should be an “=” in the place of one of the “+”

There is C = xA + yB “+”

Should be C = xA + yB “=”