Solutions to Homework
Section 1.2
#1, 3, 7, 11, 13, 17, 19, 21
1.
Study Guide:
To check whether a matrix is in echelon form, ask these questions:
(i).
Is every nonzero row above the allzero rows (if any)?
Matrix (c) fails this test, so it is NOT in echelon form.
(ii).
Are the leading entries in a stairstep pattern, with zeros below each leading entry?
Matrices (a), (b), and (d) all pass tests (i) and (ii), so they are in echelon form.
Now check to see if they
are actually in reduced echelon form…
To check whether a matrix in echelon form is actually in
reduced
echelon form, ask two more questions:
(iii).
Is there a 1 in every pivot position?
Matrix (d) fails this test, so it is only in echelon form.
Finally, ask:
(iv).
Does each leading 1 have all zeros above it (and below it)?
Matrices (a) and (b) pass all four tests, so they are in reduced echelon form.
3.
This final matrix is in reduced echelon form and the pivot positions are circled.
Original matrix:
The pivot columns are 1 and 3.
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 Spring '13
 agsmne
 Statics, Row echelon form, Closure

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