Linear Combination

26. Linear Combination

Set of vector

𝑣_{1}, 𝑣_{2}, \dots, 𝑣_{𝑛} \in ℝ^{𝑛}

Where

Linear combination of those vector

𝑐_{1} 𝑣_{1} + 𝑐_{2} 𝑣_{2} + \dots + 𝑐_{𝑛} 𝑣_{𝑛}

𝑐_{1}, 𝑐_{2}, \dots, 𝑐_{𝑛} \in ℝ

Where:

Example

\vec{𝑎} = [\begin{matrix} 1 \\ 2 \end{matrix}] \vec{𝑏} = [\begin{matrix} 0 \\ 3 \end{matrix}]

0 \vec{𝑎} + 0 \vec{𝑏}

3 \vec{𝑎} + 2 \vec{𝑏}