In this video, I give a geometric description of the solutions of Ax = b, and I prove one of my favorite theorems in linear algebra: The general solution of Ax = b is equal to the general solution of Ax = 0 plus a particular solution of Ax = b. This explains why it's so important to find the solutions of Ax = 0. I further generalize this to linear transformations, and even to differential equations! Enjoy
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