Linearly Dependent

==2024-12-11

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Dependency is a unstable.

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Theory

In simple terms, if a vector if dependent on others, it is $LD$.

Given a Set of Vectors $A$, $A$ is said to be Linearly Dependent if $\exists {\alpha }_1,{\alpha }_2,{\alpha }_3,\dots ,{\alpha }_{n_o(A)}$ such that the equation: ${\alpha }_1{a}_1+{\alpha }_2{a}_2+{\alpha }_3{a}_3+\cdots +{\alpha }_{n_o(A)}{a}_{n_o(A)}=0$ has non-trivial solution as well.

That means the scalars ${\alpha }_i$ are not all zero.

1. If one of the vectors in set $A$ can be expressed as the Linear Combination of other vectors, the set $A$ is $LD$.

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PTR