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MTH212

Question: If the transpose of A is -A, then A is said to be
Answer:  Skew symmetric

Question: Two finite ‑ dimensional vector spaces U and V are isomorphic if and only if
Answer:  dim U = dim V

Question: Let T: Uât’V be a linear transformation . T is an isomorphism (or is invertible) if it is one-one and onto, and then U and V are called
Answer:  Isomorphic spaces

Question: Linear transformations are also called â€|
Answer:  vector space homomorphisms

Question: Let \\(T: Uâf V\\) be a linear transformation. T is called â€| if, for each \\ (vâ““V,â“/ uâ~U \\)such that T(u) = v, that is
R(T) = v.
Answer:  Surjective

Question: Let U and V be vector spaces over a field F. Let \\(T: Uâf V\\)be a linear transformation. Which of the statement below is true?
Answer:  Ker T is a subspace of U and R(T) is a subspace of V

Question: Let U and V be finite-dimensional vector spaces over F. the U and V are isomorphic if and only if â€|
Answer:  dim U = dim V

Question: A number which can be expressed in the form p/q here p and q are integers and q not equal zero is called
Answer:  rational number

Question: Let U and V be vector spaces over a field F, and let T:Uâ+’V be a one-one and onto linear transformation. The T is called anâ€|
Answer:  Isomorphism between U and V

Question: Let T: UâfV be a linear transformation where U. V are of the same finite dimension. Then the following statements are equivalent. Which one of the statement is not true?
Answer:  T is homomorphism

Question: T:l)â+’V is one-one if and only if â€|
Answer:  KerT=0



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