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1.2 - Row Reduction and Echelon Form Questions and answers latest update 2024
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1.2 - Row Reduction and Echelon Form Questions and answers latest update 2024
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1.2 - Row Reduction and Echelon FormA rectangular matrix is in echelon form if it has the following three properties - correct answer1. 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 in the row above it.
3. All entries in a column below a leading entry are zeros
(Ex on pg 13)
A matrix is in reduced row echelon form if... - correct answer1. All of the conditions for echelon form are
true
2. Each leading entry in each nonzero row is 1
3. Each leading 1 is the only nonzero entry in its column
(Ex on pg 13)
Uniqueness theorem of the reduced echelon form - correct answerEach matrix is row equivalent to one
and only one reduced echelon matrix
Pivot position - correct answerA location in a matrix that corresponds to a leading 1 in the reduced
echelon form of the matrix
Pivot column - correct answerA column of a matrix that contains a pivot position
Forward phase - correct answerThe steps to get it into echelon form (kind of going from the top left
down)
Backward phase - correct answerThe steps that get the matrix into reduced row echelon form (going
from bottom right up)
Existence and Uniqueness theorem - correct answerA linear system is consistent if and only if the
rightmost column of the augmented matrix is not 0. (Basically saying there can't be a row of all zeros and
then a number in the augmented spot)
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