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*The text aims to leverage geometric intuition to enhance algebraic thinking.* In spite of the fact that it may be difficult to visualize \(\real^{1000}\text{,}\) many linear algebraic concepts may be effectively illustrated in \(\real^2\) or \(\real^3\) and the resulting intuition applied more generally. Indeed, this useful interplay between geometry and algebra illustrates another mysterious mathematical connection between seemingly disparate areas.