4_F10H4 - MATH 4 Fall 2010 Instructor: Professor R. C....

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MATH 4 Fall 2010 Instructor: Professor R. C. Reilly REMINDER: MIDTERM EXAM #1 ON FRIDAY OCTOBER 29, 2010 Assignment #4 NOTE: This assignment is for Weeks #4 and #5; it includes all the classes through the midterm exam. 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 ‘Custom Edition for UCI’. You are expected to do the assigned readings before the corresponding lectures.) Monday 10/18/2010: Section 2.3 Wednesday 10/20/2010: Section 6.1 Friday 10/22/2010: (1) Continue reading Section 6.1, but only through the end of Example 5 on Page 288. (The various applications and other material in Section 6.1 which follow Example 5 are directed towards engineers.) (2) Read the extra material that appears on Pages 3 and 4 at the back of this of this assignment. Monday 10/25/2010: Continue with Section 6.3 Wednesday 10/27/2010: Finish off any remaining material for the midterm exam; review. Friday 10/29/2010: MIDTERM EXAM 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 10/19/2010. (1) Page 97 # 2(a); 3(b,d,f); 4; 7(c,d) NOTE: In 3(d,f) use the elimination method to compute the determinants. (2) Page 105 #1 (b, c, d); 2(b, d); 4 (B) Prepare these items for the discussion on Thursday 10/21/2010: REMINDER; Quiz #2 will be held during this discussion meeting. It will cover material through Section 2.2. (1) Let A be the 3-by-3 matrix given by A = 5 - 2 4 1 0 2 - 1 6 4 . (a) Determine whether A is invertible. If it is invertible, compute A - 1 using the adjoint of A . If it is not invertible, explain how you know that this is the case. (b) Compute det ( A 5 ) without doing an enormous amount of calculation. (2) Let A = 1 2 1 0 4 3 1 2 2 (a) Compute A - 1 using the adjoint matrix adj ( A ).
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(b) Use the result of Part (a) to solve the system A x = b , where b = - 2 3 0 . (C) Prepare these items for the discussion on Tuesday 10/26/2010: (1) Go over Example 4 on Page 287 of ‘Leon’. Note that the text simply records the final – and factored – version of the characteristic polynomial in this example, namely - λ ( λ - 1) 2 ; but it gives no clue about how it arrived at this expression. Thus, I want you to compute the characteristic polynomial in two ways: (i) using the cofactor expansion of det ( A - λI ) along the first column; (ii) using the Direct 3-by-3 Formula discussed in the Extra Material at the back of this
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4_F10H4 - MATH 4 Fall 2010 Instructor: Professor R. C....

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