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1.2 Row Reduction and Echelon Forms Questions and answers latest update 2024
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1.2 Row Reduction and Echelon Forms Questions and answers latest update 2024
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1.2 Row Reduction and Echelon FormsA rectangular matrix is in echelon form if it has the following 3 properties: - correct answerAll 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 answerleftmost 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 answerthe 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 answerone and only one reduced echelon matrix
Since the reduced echelon form is unique, the leading entries are... - correct answeralways in the same
positions in any echelon form obtained from a given matrix
Pivot position - correct answera location in a matrix that corresponds to a leading 1 in the reduced
echelon form of a matrix.
Pivot column - correct answercolumn of a matrix that contains a pivot position
pivot - correct answernonzero number in a pivot position that is used as needed to create zeros via row
operations.
A linear system is consistent if and only if the ________ column of the augmented matrix is _____ a ____
_______ -- that is, if and only if an echelon form of the augmented matrix has no row of the form [ 0 ... 0
b] with b nonzero - correct answerrightmost, not, pivot column
If a linear system is consistent, then the solution set contains either (i) a ____ solution, when there are
___ _____ _________, or (ii) infinitely many solutions, when there is at least ___ ____ ________ -
correct answerunique, no free variables, one free variable
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