Linear Algebra Chapter 1.2 Study Guide Graded A+

The pivot positions in a matrix depend on whether the row interchanges are used in the row reduction process {Ans: False. If an interchange is used on a matrix in echelon form, it would no longer be in echelon form}The echelon form of a matrix is unique {Ans: False. The reduced echelon form is unique}In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations {Ans: False. each matrix is row equivalent to one and only one reduced echelon form}The row reduction algorithm applies to only the augmented matrices for a linear system {Ans: False. The row reduction algorithm applies to any matrix whether or not the matrix is viewed as an augmented matrix for a linear system. Any nonzero matrix may be row reduced}Whenever a system has free variables, the solution set contains many solutions {Ans: false}If one row in an echelon form of an augmented matrix is [0 0 0 5 0], then the associated linear system is inconsistent {Ans: False. A system is inconsistent if and only if one of its equations corresponds to an augmented matrix with