How can the linear combination of two non singular and linearly independent vectors encompass the whole of 2D euclidean space? I can't seem to intuitively understand this concept hammered by Prof. Strang in the MIT OCW. Is there any simple intuitive way or rigorous math way to understand this? Any input would be fine. Thanks!

John.

Question

How can the linear combination of two non singular and linearly independent vectors encompass the whole of 2D euclidean space? I can't seem to intuitively understand this concept hammered by Prof. Strang in the MIT OCW.  Is there any simple intuitive way or rigorous math way to understand this? Any input would be fine. Thanks!

John.

anonymous · Answer

Did you watch the video posted on this topic by MIT open courseware

anonymous · Answer

The professor clearly explains this topic, and also moves to n dimension

anonymous · Answer

Do you happen to remember which lecture? Coz, he doesn't explain it in the first one which I'm watching..

anonymous · Answer

I think its in the most introductory one

anonymous · Answer

I may be wrong

anonymous · Answer

hmm.. lemme give a go at the rest too then... thanks!

anonymous · Answer

You can think on it like this (I don't want to tell you more than this, since it will spoil the real fun of it), it represents any point on the 2 d plane. 
Think on it...

anonymous · Answer

Finally, got it... understood it graphically. Its beautiful! Thanks for your hints.