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Chapter 5 Subspaces of \(\R^n\)
Objectives
Determine whether sets are closed under addition and/or scalar multiplication.
Determine whether a set of vectors is a basis of a subspace or \(\R^n\text{.}\)
Write the coordinates of a vector with respect to a given basis of \(\R^n\text{.}\)
Identify the dimension of the span of a given set of vectors.
Find a basis for each of the following: the row space, the column space, and the null space of a given matrix.
Prove elementary theorems concerning rank of a matrix and the relationship between rank and nullity.
