Prof. X has two brilliant students Y and Z in his class. He introduces the concept...

Prof. X has two brilliant students Y and Z in his class. He introduces the
concept of vector spaces, bases and dimension in his 5th session. As an exercise,
he gives a vector space V of dimension n and asks Y and Z to find a basis. Y
produces a set S with n elements. But Z being lazy, takes the set S, removes
a vector and adds a new vector to it creating a new set T. Prof. X looks at set
T and confirms to class that it is a basis. He then asks the class if the set S
produced by Y could be a basis without telling them what it is. While student
U says yes, student W says need not and Prof. X says that both U and W
could be correct. Justify the statement of Prof. X with suitable examples of V
over F, n, S and T.

Expert Solution

You can generalise this as well by taking Rⁿn(R) . If you want me to do that comment down and if you were able to understand the explanation please give feedback

Colby Messinger answered 1 year ago

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