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You have to keep refreshing the page.Brian_D said:
The vectors should be columns in your matrix. It doesn't work if you make the vectors the rows. You should check this yourself.Brian_D said:
Conflicting definitions of linear independence
- Thread starter Brian_D
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Confusion arises from the definitions of linear independence, particularly when considering a set of vectors that includes a zero vector or is underdetermined. The key point is that a set of vectors is linearly independent if the only solution to the equation formed by their linear combination equating to zero is the trivial solution, where all coefficients are zero. In the discussed case, the presence of a zero column implies that there are infinitely many solutions, contradicting the notion of linear independence. Thus, while the textbook may suggest the vectors are independent based on the first three variables, the inclusion of a zero vector or an underdetermined system ultimately indicates linear dependence. Understanding these distinctions clarifies the apparent paradox in definitions of linear independence.
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