laqf07f_sg_Chap_5 - Linear Algebra, Fall 2007...

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Linear Algebra, Fall 2007 (http://www.math.nthu.edu.tw/˜ wangwc/) Study Guide for Chapter 5 1. Section 5.1: (a) Pay attention to scalar and vector projection of x onto y . (b) Skip Application 1,3 . Read Application 2. 2. Section 5.2: (a) Study the proof of Theorem 5.2.1 and how to use it to compute R ( A ) and N ( A ). (b) Study the definition of ’direct sum’ and its equivalent statement. (c) Remember the trick that we use to prove S S = 0 . 3. Section 5.3: (a) Must know how to solve for the least square solution for an over-determined system. (b) Understand the meaning of ”least square” in a least square problem. (c) Compute an example of least square solution of A x = b where A ∈ M m,n with m > n and rank( A ) < n . (d) Given a set of data, study how to obtain an over-determined system of equations from best square fit by a linear function, a quadratic function, etc. 4. Section 5.4: (a) Remember the definition of inner product and norm. (b) Remember an non-standard inner product on
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laqf07f_sg_Chap_5 - Linear Algebra, Fall 2007...

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