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If, in a matrix, there is a column of all zeros, does this mean the given vector/matrix is linearly dependent?

An example would be:

[1 2 0 4]

[2 3 0 1]

[5 2 0 7]

A few questions to clear up some possible misconceptions:

1) The matrix above is a 4-dimensional vector?

2) The given vector has 4 unknowns, but a column of zeros, therefore the system is linearly dependent.

Thanks for your help!!!

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# Linear independence if there is a column of zeros

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