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I am solving a problem in the form: (A^{T}x=0 where A is a matrix of known numbers and I am solving for x. After performing reduction and multiplying A^{T}x, I am left with the following equations:

-X_{1}+ X_{4}- X_{5}= 0

-X_{2}+ X_{4}= 0

-X_{3}+ X_{4}-X_{5}+ 28X_{6}= 0

From these equations, I am trying to find the linearly independent vectors however, I am not sure how to do this. I tried pulling out a linear book but I couldn't make straight forward sense of the procedure. Can anyone help me out? Thanks!

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# Linear Algerba - Finding linearly independent vectors

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