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I am studying the linear Independence and linear dependence of the vectors in my Linear algebra course and i am confused about the following theorem (The book is Linear Algebra and its applications by David C Lay) and i need some explanation of this theorem. enter image description here

In this theorem i am confused about "If S is linearly dependent and V1 not equal to zero then some Vj (with j>1) is a linear combination of the preceeding vectors"

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