Linear Algebra 129, sums in vector spaces

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So, I have a commentary. After reading some textbooks, I kind of understood SUM of Subspaces. However, something was not clear, because "adding" is not the addition as we do on the real line, for example. Therefore, in the end of the video, you said "so, U + W is the sum of this two matrices". And you wrote the result. But this is the most important point of the video!! You need to show us WHY the result is that one! WHY is a from one matrix is not "adding" to the a in the other matrix! This is where all students' doubts lie. Would you please explain the intuition behind adding those two matrices and finding that result? Thank you!

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