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5.5 In this section we shall study three important vector spaces that are associated
with matrices. Our work here will provide us with a deeper understanding of the
ROW SPACE, COLUMN relationships between the solutions of a linear system of equations and
SPACE, AND NULLSPACE properties of its coefficient matrix.
We begin with some definitions.
DEFINITION
For an matrix
the vectors
in formed from the rows of A are called the row vectors of A, and the vectors
in formed from the columns of A are called the column vectors of A.
EXAMPLE 1 Row and Column Vectors in a Matrix
Let
The row vectors of A are
and the column vectors of A are
The following definition defines three important vector spaces associated with a matrix.
