MATH235 Chapter : Math235.pdf
1 Oct 2013
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Document Summary
The main purpose of this chapter is to review a few important concepts from the. These concepts include subspaces, bases, dimension, and linear mappings. As you will soon see the rest of the book relies heavily on these and other concepts from the rst six chapters. Recall from math 136 the four fundamental subspaces of a matrix. Then col(a) and null(at ) are subspaces of rm and row(a) and null(a) are subspaces of rn. Our goal now is to nd an easy way to determine a basis for each of the four funda- mental subspaces. To help you understand the following two proofs, you may wish to pick a simple 3 2 matrix a and follow the steps of the proof with your matrix a. The columns of a which correspond to leading ones in the reduced row echelon form of a form a basis for col(a).
