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1.2 - Row Reduction and Echelon Form Questions and answers latest update 2024 $12.99   Add to cart

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1.2 - Row Reduction and Echelon Form Questions and answers latest update 2024

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  • Echelon
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  • Echelon

1.2 - Row Reduction and Echelon Form Questions and answers latest update 2024

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  • February 27, 2024
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  • 2023/2024
  • Exam (elaborations)
  • Questions & answers
  • Echelon
  • Echelon
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1.2 - Row Reduction and Echelon Form
A 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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