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I have hard time understanding the concept of vector, matriecs in relation with rank and independent/dependent columns / rows.

I have two question that I would like to have help:

The set of vectors {v_{1},v_{2},v_{3},v_{4}} would be linearly dependent if

1-v_{3}is the zero vector

2- each of the vectors is in R^{3}

3- the row reduced form of the matrix whose columns are the given vectors has rank less than 4

4-the row reduced form of the matrix whose rows are the given vectors has rank less than 4

5- any of the above would imply dependence

I would chose 3 or 4:

Please can you help me to define the expressions "the row reduced form of the matrix whose columns are the given vectors"

Is that means that the matrix would be like

[a b c d]

[e f g h]

[i j k l ]

wherea,e,iare the coordinates of v_{1}

b,f,jare components of v_{2}

c,g,kare components of v_{3}

d,h,lare components of v_{4}?

Thank you very much

B.

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# Homework Help: Understanding the concept of vector

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