[線代] linearly independent

[mqazz1 (無法顯示)]

let β ={    x1,     x2, ...,     xn} be a subset of V, and

let β'={x1+2x2, x2+2x3, ..., xn+2x1}, where n>=3

then, β is linearly independent if and only if β' is linearly independent


請問這個要怎麼證呢?

謝謝

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