Ch.1.2- Row Reduction And Echelon Forms Exam Questions & Detailed Answers

CH.1.2- ROW REDUCTION AND ECHELON FORMS
EXAM QUESTIONS & DETAILED ANSWERS
1. What is a "leading The leftmost nonzero entry (in a nonzero row)
entry of a row"?

2. What is the If the matrix has the following three properties:
DE- FINITION
1.2 of 1. All nonzero rows are above any rows of all zeros.
of a
rectangular 2. Each leading entry of a row is in a column to the right of the
matrix in leading entry of the
"Eche- lon row above
it.
form" or "Row
echelon
form"?
3. All entries in a column below a leading entry are zeros.




3. What is the The matrix satisfies the definition of echelon form as well as the following two
def- inition of conditions.
"re- duced
echelon 1. The entry in each nonzero row is 1
form" or "re-
duced row 2. Each leading 1 is the only nonzero entry in its column.
eche- lon
form"?
A matrix that is in echelon form.

4. What is an
"eche- lon
matrix"?

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, CH.1.2- ROW REDUCTION AND ECHELON FORMS
EXAM QUESTIONS & DETAILED ANSWERS
5. What is a reduced One that is in reduced echelon form.
echelon matrix?

6. Any nonzero Row reduced, that is transformed by elementary row operations into
ma- trix may more than one matrix in echelon form, using ditterent sequences of row
be..? operations.
7. What is THEO- It is the Uniqueness of the Reduced Echelon form:
REM 1 of Row
Re- Each matrix row is equivalent to one and only one reduced echelon
matrix.




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