6.5.1 Example of Linear Dependent Set

Types: N/A
Examples: N/A
Constructions: N/A
Generalizations: 6.5 Theorem of Vector List Size m x 1

Properties: N/A
Sufficiencies: N/A
Questions: N/A

Linearly Dependent Set

Let's confirm ${a_{k}}_{k = 1}^{3}$ is linearly dependent.

\begin{aligned} {\vec{a}}_{1} = [\begin{array}{c} 5 \\ 0 \\ 0 \\ 5 \end{array}], & {\vec{a}}_{2} = [\begin{array}{c} 0 \\ - 1 \\ - 1 \\ 0 \end{array}], & {\vec{a}}_{3} = [\begin{array}{c} 4 \\ 4 \\ 4 \\ 4 \end{array}] \end{aligned}

Solution.

\begin{aligned} {\vec{a}}_{3} & = [\begin{array}{c} 4 \\ 4 \\ 4 \\ 4 \end{array}] = \frac{4}{5} [\begin{array}{c} 5 \\ 0 \\ 0 \\ 5 \end{array}] + - 4 [\begin{array}{c} 0 \\ - 1 \\ - 1 \\ 0 \end{array}] = [\begin{array}{c} 4 \\ 0 \\ 0 \\ 4 \end{array}] + [\begin{array}{c} 0 \\ 4 \\ 4 \\ 0 \end{array}] \end{aligned}