# Chapter 1 - Linear Equations in Linear Algebra - 1.2 Exercises: 2

a) reduced row echelon form b) echelon form c) neither echelon form nor reduced row echelon form d) echelon form

#### Work Step by Step

a) The matrix is in reduced row echelon form because all its leading entries are 1, and all leading entries are the only non-zero entries in their columns. Column three, which has two non-zero entries, does not have a leading entry, meaning that the system has one free variable. b) The matrix is in echelon form because, although all leading entries are the only non-zero entries in their columns, said leading entries are not all 1 (specifically the leading entry in the second row.) c) The matrix does not contain the property of all all nonzero rows being above any rows of all zeros, and is therefore in neither echelon form nor reduced row echelon form. d) The matrix is only in echelon form, because it does not contain the property of all leading entries being the only non-zero entries in their columns (specifically in column three.)

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