2. Suppose u, U2,, Un are independent vectors in R. Let k 0 be a real...

 

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2. Suppose u₁, U2,, Un are independent vectors in R". Let k 0 be a real number. Show that then, the vectors below are also independent: v₁ = k²u₁ - ku2, v₂ = k³ u₂ −k² uz, V3 = k¹u3 - k³u4, v₂ = k¹+¹ui — k¹u₁+1, i+1, Vi Un-1 = kn Un-1 kn+1 un• Un = -kn- Ung 2. Suppose u₁, U2,, Un are independent vectors in R". Let k 0 be a real number. Show that then, the vectors below are also independent: v₁ = k²u₁ - ku2, v₂ = k³ u₂ −k² uz, V3 = k¹u3 - k³u4, v₂ = k¹+¹ui — k¹u₁+1, i+1, Vi Un-1 = kn Un-1 kn+1 un• Un = -kn- Ung

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ANSWER To show that the vectors v1 v2 v3 vn are independent we need to show that the only linear com... View the full answer