1.2- ECHELON FORM EXAM
QUESTIONS & DETAILED CORRECT
ANSWERS
row echelon form - Correct Answer ✔✔ The form of a matrix with the following
properties: 1. All nonzero rows are above any rows of all zeros. 2. Each leading entry of
a row is in a column to the right of the leading entry of the row above it. 3. All entries in
a column below a leading entry are zeros.
reduced row echelon form - Correct Answer ✔✔ The form of a matrix with the properties
of row echelon form as well as: 1. The leading entry in each nonzero row is 1 and 2.
Each leading 1 is the only nonzero entry in its column.
echelon matrix - Correct Answer ✔✔ A matrix in echelon form
reduced echelon matrix - Correct Answer ✔✔ A matrix in reduced echelon form
row reduction - Correct Answer ✔✔ Transformation by elementary row operations
pivot position - Correct Answer ✔✔ a location in matrix A that corresponds to a leading
1 in the reduced echelon form of A
pivot column - Correct Answer ✔✔ a column of matrix A that contains a pivot position
pivot - Correct Answer ✔✔ a nonzero number in a pivot position that is used as needed
to create zeros via row operations
forward phase - Correct Answer ✔✔ phase of the row reduction algorithm that reduces
a matrix to echelon form
backward phase - Correct Answer ✔✔ phase of the row reduction algorithm that
reduces a matrix in echelon form to a reduced echelon form
basic variables - Correct Answer ✔✔ variables that correspond to pivot columns in a
matrix
free variables - Correct Answer ✔✔ variables that do not correspond to pivot columns in
a matrix
general solution - Correct Answer ✔✔ a parametric description of a solution set that
expresses the basic variables in terms of the free variables (the parameters), if any; can
be written in vector form
QUESTIONS & DETAILED CORRECT
ANSWERS
row echelon form - Correct Answer ✔✔ The form of a matrix with the following
properties: 1. All nonzero rows are above any rows of all zeros. 2. Each leading entry of
a row is in a column to the right of the leading entry of the row above it. 3. All entries in
a column below a leading entry are zeros.
reduced row echelon form - Correct Answer ✔✔ The form of a matrix with the properties
of row echelon form as well as: 1. The leading entry in each nonzero row is 1 and 2.
Each leading 1 is the only nonzero entry in its column.
echelon matrix - Correct Answer ✔✔ A matrix in echelon form
reduced echelon matrix - Correct Answer ✔✔ A matrix in reduced echelon form
row reduction - Correct Answer ✔✔ Transformation by elementary row operations
pivot position - Correct Answer ✔✔ a location in matrix A that corresponds to a leading
1 in the reduced echelon form of A
pivot column - Correct Answer ✔✔ a column of matrix A that contains a pivot position
pivot - Correct Answer ✔✔ a nonzero number in a pivot position that is used as needed
to create zeros via row operations
forward phase - Correct Answer ✔✔ phase of the row reduction algorithm that reduces
a matrix to echelon form
backward phase - Correct Answer ✔✔ phase of the row reduction algorithm that
reduces a matrix in echelon form to a reduced echelon form
basic variables - Correct Answer ✔✔ variables that correspond to pivot columns in a
matrix
free variables - Correct Answer ✔✔ variables that do not correspond to pivot columns in
a matrix
general solution - Correct Answer ✔✔ a parametric description of a solution set that
expresses the basic variables in terms of the free variables (the parameters), if any; can
be written in vector form
