Linear Algebra Example Problems - Linearly Independent Vectors #1

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Given a set of vectors we want to determine if they are linearly independent or not (i.e. linear dependent). A set of vectors is linearly independent when the linear combination of the vectors is equal to an all-zero vector only in the trivial case when all combining coefficients are zero.

Thus, to determine if a set of vectors is linearly independent, we just have to construct and solve a homogeneous system of equations. If the only solution is the trivial solution, the vectors are linearly independent. If there are more solutions than just the trivial solution, the vectors are linearly dependent.

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[baueranthony]

This is great and really helpful! The spanning videos really help to. To go one step further for my understanding, if I wanted to determine if these three vectors form a basis for R3, all we'd need to find if they span all of R3?

[Adam-gpij]

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[gaddiji]

how to do this, augmented matrix and row reduction thing?

[sayanbaidya]

can prove just by seeing det not equal to 0 ?

[kushagrasonkar]

Hi. Awesome tutorial. Can you please link the row reduction video here or in the description please?

[toheedh]

what if its a 4x4 ?
is it the same case as in video