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.

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

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

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