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laqf07f_sg_Chap_1 - 2 Section 1.3(a Know how to perform...

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Linear Algebra, Fall 2007 (http://www.math.nthu.edu.tw/˜ wangwc/) Study Guide for Chapter 1 1. Section 1.1-1.2: (a) Understand and remember the meanings of ’row’ and ’column’. (b) Understand and remember the indexing rules of a matrix. (c) Understand the meanings of ’row echelon form’ and ’reduced row echelon form’. (d) Be able to determine whether a matrix is in ’(reduced) row echelon form’ or not. (e) Know how to put a matrix into ’row echelon form’ or ’reduced row echelon form’ by way of ’elementary row operations’. Write down a matrix at random and try to put it into (reduced) row echelon form. (f) Know whether an augmented matrix in (reduced) row echelon form is consistent or inconsistent and why Theorem 1.2.1 holds. (g) If consistent, you should know how to select the ’lead variables’ and ’free variables’, then solve the lead variables in terms of free variables and the right hand side. (h) Read Applications 1, 4 and skip Applications 2, 3 in section 1.2.
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Unformatted text preview: 2. Section 1.3: (a) Know how to perform matrix-vector and matrix matrix multiplication. (b) Read carefully on the proof of Theorem 1.3.1. Pay attention to the choice of the indices. (c) Be ware of the fact that AB 6 = BA in general. Find an example and keep it in mind. (d) Read Application 1, 2. Skip Application 3, 4, 5. 3. Section 1.4: (a) Know how to find the inverse of an elementary matrix. (b) Know the exact correspondence between an elementary matrix and an elementary row (column) operation. (c) Read Theorem 1.4.2 (equivalent conditions for non-singularity) and study its proof. (d) Know how to perform ’ LU factorization’ and its relation with ’Gauss elimination’. 4. Section 1.5: (a) Understand and remember the meaning of a ( i, :). (b) Know how to express AB in terms of A b j and a ( i, :) B (page 73). (c) Know how to express AB in terms of sub-blocks of A and B . 1...
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