Linearly independent vectors with examples
https://www.mathbootcamps.com/linearly-independent-vectors-examples/
The Formal Definition of Linear IndependenceExamples of Determining When Vectors Are Linearly IndependentProperties of Linearly Independent Vectors A set of vectors is linearly independent if and only if the equation: c1v→1+c2v→2+⋯+ckv→k=0→ has only the trivial solution. What that means is that these vectors are linearly independent when c1=c2=⋯=ck=0is the only possible solution to that vector equation. If a set of vectors is not linearly independent, we say that they are linearly dependent. …
A set of vectors is linearly independent if and only if the equation: c1v→1+c2v→2+⋯+ckv→k=0→ has only the trivial solution. What that means is that these vectors are linearly independent when c1=c2=⋯=ck=0is the only possible solution to that vector equation. If a set of vectors is not linearly independent, we say that they are linearly dependent. …
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