This is alot so if you want to break it into two repsonsesthat would be ok and I

Question

This is alot so if you want to break it into two repsonsesthat would be ok and I will give lifesaver karma points for allresponses. Than you so much. 1.) Let V be a vector space and W = v1,...vn. Prove thaspan(W) is a subspace of V. 2.)Consider the vector space R^3. Let V = {(1,2,-1), (1,1,0),(1,0,1)}. For each of the following questions, please give clearjustifications for your answers. A.) Is V linearly independent? B.) Is w = (2,1,1) in span(V)? C.) Find span(V). Does V spans R^3? 3.)For what values(s) of is the set of vectors(^2 - 5,1,0), (2,-2,3), (2,3,-3) linearly independent? 4.) Let the set {v1,v2} be linearly dependent. Prove that {v1+ 2v2,3v1-v2} is also linearly dependent. 5.) State (with brief explanation) whetherthe following statements are true or false. A.) all vectors of the form (a,0,-1) form a subspace ofR^3. B.) Every set of vectors in R^3 containing two vectors islinearly independent. C.)Every set of vectors spanning M2,3 contains at least 6vectors. D.)If {v1,v2} is a linealy dependent set, then each vector isa scalar mulitiple of the other. E.) If {v1,v2,v3} is a linearly independent set, then so isthe set {kv1,kv2,kv3} for any nonzero scalar k. This is alot so if you want to break it into two repsonsesthat would be ok and I will give lifesaver karma points for allresponses. Than you so much. 1.) Let V be a vector space and W = v1,...vn. Prove thaspan(W) is a subspace of V. 2.)Consider the vector space R^3. Let V = {(1,2,-1), (1,1,0),(1,0,1)}. For each of the following questions, please give clearjustifications for your answers. A.) Is V linearly independent? B.) Is w = (2,1,1) in span(V)? C.) Find span(V). Does V spans R^3? 3.)For what values(s) of is the set of vectors(^2 - 5,1,0), (2,-2,3), (2,3,-3) linearly independent? 4.) Let the set {v1,v2} be linearly dependent. Prove that {v1+ 2v2,3v1-v2} is also linearly dependent. 5.) State (with brief explanation) whetherthe following statements are true or false. A.) all vectors of the form (a,0,-1) form a subspace ofR^3. B.) Every set of vectors in R^3 containing two vectors islinearly independent. C.)Every set of vectors spanning M2,3 contains at least 6vectors. D.)If {v1,v2} is a linealy dependent set, then each vector isa scalar mulitiple of the other. E.) If {v1,v2,v3} is a linearly independent set, then so isthe set {kv1,kv2,kv3} for any nonzero scalar k.

Explanation / Answer

I did not know there is a time limit for giving karma pointsGunsh. I found the answer in the book but I still wanted to giveyou lifesaver points for your effort. I will do it sooner nexttime. Thank you anyways, U.W.

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