(Note: Unless stated otherwise, all section and page numbers refer to the
textbook for this part of the course, ‘Linear Algebra and Applications (8th edition)’, by S. Leon, or
the corresponding ‘Third Custom Edition for UCI’. You are expected to do the assigned readings
the corresponding lectures.)
Monday 10/04/2010: Section 1.3 and start of Section 1.4
Wednesday 10/06/2010: Finish Section 1.4
Friday 10/08/2010: Read a one-page document, called ‘Computing the Inverse of an
which appears at the back of this assignment.
Things to Prepare for the Discussions
Note: These are problems/examples/topics which the Teaching Assistants (TAs) will cover in the
discussion sections. You are expected to work on them
you go to the discussions.
(A) Prepare these items for the discussion on Tuesday 10/05/2010.
(1) Page 25 # 12. Please do this problem two ways:
(a) The way the text asks you to follow; namely by computing the row-echelon form of a
3-by-5 augmented matrix [
], and then doing back substitution twice.
(b) By computing the
row-echelon form of the matrix [
] used above.
In the ﬁrst couple of sections, the text expresses solutions of systems as horizontal
strings of numbers. However, starting in Section 1.3 the text insists – and so do I – that you always
express solutions as
of numbers, not rows; that is, as column vectors. This is simply the
accepted way of representing such solutions in modern linear algebra, so even if it seems silly, we all
have to put up with it. You might as well get used to it and start doing it now, even in problems
coming from Section 1.2.
(2) In the lecture on Friday October 1, we discussed Example 5(b) on Pages 15-16, and obtained
the same solution as given in the text, except that I used the free-variables
introducing new letters
(and Greek letters at that!) as the text does.
Express this solution in the form
column vectors; that is, vectors whose entries do not depend on the free variables
In the preceding I ask you to express the general solution of a particular system as a
sum of of vectors of the following type: the ﬁrst vector is a constant vector; as for the remaining
vectors in the sum, there is one for each free variable, and it is of the form of a nonzero constant
vector multiplied by that free variable. Whenever the general solution of a system is written that
way, we say the solution is in