Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in reduced row-echelon form. 0 0 1 0 0 0 0 0 1 0 LO 007 STEP 1: Check rows consisting entirely of zeros. Do all rows (if any) consisting entirely of zeros occur at the bottom of the matrix? O Yes O No O There are no rows consisting entirely of zeros. STEP 2: Check the first nonzero entry of each row. Does each row that does not consist entirely of zeros have the first nonzero entry equal to 1? O Yes O No O There are no rows that do not consist entirely of zeros. STEP 3: Check successive nonzero rows. If each nonzero row has a leading 1, is the leading 1 in the higher row farther to the left of the leading 1 in the lower row for each pair of successive rows? O Yes O No O There exists at least one row which does not have a leading 1. STEP 4: Check the columns with leading ones. Does every column with a leading 1 have zeros in every position above and below its leading 1? O Yes O No STEP 5: Determine the form of the matrix. (Select all that apply.) Orow-echelon form O reduced row-echelon form Oneither

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in reduced row-echelon form.
0 0 1 0 0
0 0 0 1 0
LO 007
STEP 1: Check rows consisting entirely of zeros.
Do all rows (if any) consisting entirely of zeros occur at the bottom of the matrix?
O Yes
O No
O There are no rows consisting entirely of zeros.
STEP 2: Check the first nonzero entry of each row.
Does each row that does not consist entirely of zeros have the first nonzero entry equal to 1?
O Yes
O No
O There are no rows that do not consist entirely of zeros.
STEP 3: Check successive nonzero rows.
If each nonzero row has a leading 1, is the leading 1 in the higher row farther to the left of the leading 1 in the lower row for each pair of successive rows?
O Yes
O No
O There exists at least one row which does not have a leading 1.
STEP 4: Check the columns with leading ones.
Does every column with a leading 1 have zeros in every position above and below its leading 1?
O Yes
O No
STEP 5: Determine the form of the matrix. (Select all that apply.)
Orow-echelon form
O reduced row-echelon form
Oneither
Transcribed Image Text:Determine whether the matrix is in row-echelon form. If it is, determine whether it is also in reduced row-echelon form. 0 0 1 0 0 0 0 0 1 0 LO 007 STEP 1: Check rows consisting entirely of zeros. Do all rows (if any) consisting entirely of zeros occur at the bottom of the matrix? O Yes O No O There are no rows consisting entirely of zeros. STEP 2: Check the first nonzero entry of each row. Does each row that does not consist entirely of zeros have the first nonzero entry equal to 1? O Yes O No O There are no rows that do not consist entirely of zeros. STEP 3: Check successive nonzero rows. If each nonzero row has a leading 1, is the leading 1 in the higher row farther to the left of the leading 1 in the lower row for each pair of successive rows? O Yes O No O There exists at least one row which does not have a leading 1. STEP 4: Check the columns with leading ones. Does every column with a leading 1 have zeros in every position above and below its leading 1? O Yes O No STEP 5: Determine the form of the matrix. (Select all that apply.) Orow-echelon form O reduced row-echelon form Oneither
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