Solution Found!
Let Vi,V2, ,vk,v be vectors in a vector space V, and define Wi = span({vi,v2,...,vk})
Chapter 1, Problem 23(choose chapter or problem)
Let Vi,V2, ,vk,v be vectors in a vector space V, and define Wi = span({vi,v2,...,vk}), and W2 = span({vi,v2,... ,vk,v}). (a) Find necessary and sufficient conditions on v such that dim(Wi) = dim(W2). (b) State and prove a relationship involving dim(Wi) and dim(W2) in the case that dim(Wi) ^ dim(W2)
Questions & Answers
QUESTION:
Let Vi,V2, ,vk,v be vectors in a vector space V, and define Wi = span({vi,v2,...,vk}), and W2 = span({vi,v2,... ,vk,v}). (a) Find necessary and sufficient conditions on v such that dim(Wi) = dim(W2). (b) State and prove a relationship involving dim(Wi) and dim(W2) in the case that dim(Wi) ^ dim(W2)
ANSWER:Step 1 of 3
Vector Space: Any given set of vectors can be considered as the Vector space which allowed the number of mathematical operation to be performed in it like addition or multiplication.