1.2 Row Reduction and Echelon Forms questions with correct answers

A rectangular matrix is in echelon form if it has the following 3 properties: - Correct Answer-All nonzero rows are above any rows of all zeros; each leading entry of a row is in a column to the right of the leading entry of the row above it; all entries in a column below a leading entry are zeros. leading entry - Correct Answer-leftmost nonzero entry in a nonzero row If a matrix in echelon form satisfies the following additional conditions, then it is in reduced echelon form - Correct Answer-the leading entry in each nonzero row is 1; each leading 1 is the only nonzero entry in its column. Each matrix is row equivalent to... - Correct Answer-one and only one reduced echelon matrix Since the reduced echelon form is unique, the leading entries are... - Correct Answer-always in the same positions in any echelon form obtained from a given matrix Pivot position - Correct Answer-a location in a matrix that corresponds to a leading 1 in the reduced echelon form of a matrix. Pivot column - Correct Answer-column