For each of the following statements, if the statement is true, write true next
ID: 3013531 • Letter: F
Question
For each of the following statements, if the statement is true, write true next to the statement; if the statement is false, write false next to the statement. If T:V rightarrow W is a linear transformation. then nullity(T) + rank(T) = dim(W). If there exists a set, {v^rightarrow_1, V^rightarrow_2, ...., v^rightarrow_5}, that spans the vector space V, then dim(V) lessthanorequalto 5. If v^rightarrow and w^rightarrow are eigenvectors corresponding to distinct eigenvalues, then {v^rightarrow, w^rightarrow) is a linearly independent set. For an n times n matrix A, det A = (-1)det A^T.Explanation / Answer
statement (a) is True
statement(b) is false, dim(v) =5
statement(c) is true
statement(d) is false det(A) = det(AT)
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