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Linear Combination in @@R^2@@ (2李⑥썝?곸쓽 ?쇱감寃고빀)



Linear Combination
Suppose that @@K@@ is a field (for example, the real numbers) and @@V@@ is a vector space over @@K@@. As usual, we call elements of @@V@@ vectors and call elements of @@K@@ scalars. If @@\textbf{v}_1,\ldots ,\textbf{v}_n@@ are vectors and @@a_1,...,a_n@@ are scalars, then the linear combination of those vectors with those scalars as coefficients is
@@a_1 \textbf{v} _1 + a_2 \textbf{v}_2 + \cdots + a_n \textbf{v}_n@@