Imagine we have 3 vectors in space. At first, they seem to be completely unrelated to each other, but look closely. When we define them with these specific coordinates, then (technically) we can observe a hidden structure. Can you tell which?
Your answer, here, will show whether or not you have the necessary intuition to speak the “language” of linear algebra. So, let me rephrase the question:
When you put these 3 vectors together, do they actually generate all of the 3D space around them?
Watch the answer here
The PDF is accompanied by this video.
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This PDF will give you an intuitive introduction to the language of linear algebra. It helps you understand how ideas like vectors, vector spaces, span, basis vectors, linear combinations, linear dependence, systems of equations, matrices, and dot products fit together. It’s the source for developing visual intuition through concrete examples, geometric explanations, guided exercises and interactive graphs.
In any case, if you don’t have the means, we always have our free videos. Thanks again!
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