Main Points
Vectors can be added together by adding the all the x components together and all the y components together. Multiples of vectors can be added together to match another vector. The multiple used can be found by changing the i and j values into constants being multiplied by the variable to equal the final vector value. If the vectors are parallel, then there is no solution. This same method can also be applied in three dimensions and with many different vectors. The span of a vector, or sum of vectors, is represented by all possible multiples of the vector. A subspace is a list of vectors that is the span of another list of vectors. The dimension of a subspace is the minimum number of vectors it takes to span that subspace.
Challenges:
The biggest challenge for me is keeping all of the columns and rows and how they multiply straight in my head. Also I thought some of the applications of spanning were quite confusing. The example using a span to solve for an equation was hard to follow. Hearing the explanation in a human voice will help.
Reflections
I had no idea vectors could be used for so damn much! I guess my only reflection is that I really hope that these concepts have some translation into the real world because vectors aren't my strong point.
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