Let V be a vector space and let X, X2, X3, , Y2 EV. Suppose that...

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Let V be a vector space and let X₁, X2, X3, №₁, Y2 EV. Suppose that both the list X₁, X2, X3, and the list y₁, y₂ are linearly independent. Prove that the list X₁, X2, X3, №₁, №₂ is linearly independent iff span{X₁, X2, X3} span{y₁, №₂} = {0}. Let V be a vector space and let X₁, X2, X3, №₁, Y2 EV. Suppose that both the list X₁, X2, X3, and the list y₁, y₂ are linearly independent. Prove that the list X₁, X2, X3, №₁, №₂ is linearly independent iff span{X₁, X2, X3} span{y₁, №₂} = {0}.