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Section 2.2 Terminology and notation
- row echelon form
a matrix that has the following properties:
if a row has nonzero entries, its first nonzero entry is a one (called a leading one),
each leading one occurs in a column that is to the right of the column containing the leading one in the row above it, and
zero rows appear below all nonzero rows
- reduced row echelon form
a row echelon form matrix that also has the following property:
- row reduction
the process of using elementary row operations to reduce a matrix to REF or RREF
- row equivalent matrices
matrices where it is possible to obtain one from the other through a sequence of elementary row operations
- rank
the number of leading ones in the RREF of the matrix
- leading variables
the variables in a linear system whose columns in the RREF of the augmented matrix contain the leading one of some row
- free variables
the variables in a linear system that are not leading variables
- general solution
a set of parametric equations from which all solutions to a linear system can be obtain by choosing arbitrary values for the parameters
- homogeneous system
a linear system in which the “equals” column is all zeros
- coefficient matrix
the matrix for a linear system but without the “equals” column
- trivial solution
the obvious solution to a homogeneous system obtained by setting all variables to equal zero
- nontrivial solution
a solution to a homogeneous system that is not the trivial solution
