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#### esis

##### New member

- Feb 4, 2014

- 10

I am working my way through Gilbert Strang's book on linear algebra. I came across a set of solutions to the problems whose solutions are not listed in the book here. However, as I was working on the following question:

I became confused by the solution provided in the link above.

I solved the problem by setting c = d, which results in a line that passes right through origo (0,0) and straight through the first and third quadrants (i.e. (-)(-) and (+)(+)).

However, in the list of solution above, they state that:

"All vectors cv + dw are on the line passing through (0,0)...".

I am confused by this, as, for example, the vector 1/3v + w, or any combination of c and d where c does not equal d would not pass through this line. Indeed, I can imagine an unlimited amount of lines that pass through origo (0,0), but which are not on the line where c = d.

I suppose I am misunderstanding the difference between lines and vectors somehow?

Thank you!