[線代] linearly independent

[mqazz1 (無法顯示)]

let x1, x2 and x3 be linearly independent vectors in R^n and let

y1 = x1 + x2

y2 = x2 + x3

y3 = x3 + x1


are y1, y2, and y3 linearly independent?


請問這個敘述是對的還是錯的?

應該怎麼證明呢?

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推 MaaLong     :用 k1*y1+k2*y2+k3*y3=0 證明係數都是零就好
推 WJAider     :同樓上，by定義即可