4_F10H2 - Assignment#2 Reading Assignments(Note Unless...

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Assignment #2 Reading Assignments (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 before 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 n × n Matrix’, 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 before 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 [ A | B ], and then doing back substitution twice. (b) By computing the reduced row-echelon form of the matrix [ A | B ] used above. Warning 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 columns 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 x 2 and x 3 instead of introducing new letters α and β (and Greek letters at that!) as the text does. Problem Express this solution in the form x = c + x 2 u + x 3 v , where c , u and v are constant column vectors; that is, vectors whose entries do not depend on the free variables x 2 and x 3 . Remark 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
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4_F10H2 - Assignment#2 Reading Assignments(Note Unless...

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