Ma351-2005 - MA 351 Elementary Linear Algebra Purdue University Edray Herber Goins January 2005 May 2005 Contents 1 Lecture 1 Monday January 10 8

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Unformatted text preview: MA 351: Elementary Linear Algebra Purdue University Edray Herber Goins January 2005 - May 2005 Contents 1 Lecture 1: Monday, January 10 8 1.1 Course Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.1 Instructor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.2 Meeting Times . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.3 Textbook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.4 Homework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.1.5 Grading Policy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 The Vector Space of m × n Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Row and Column Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Matrix Addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.5 Scalar Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2 Lecture 2: Wednesday, January 12 12 2.1 The Space R n . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2 Linear Combinations and Linear Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Linear Dependence and Linear Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3 Lecture 3: Friday, January 14 15 3.1 Linear Dependence and Linear Independence (cont’d) . . . . . . . . . . . . . . . . . . . . . . 15 3.2 Geometric Significance of Linear Independence . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.3 The Span of a Set . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.4 What is a Vector Space? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 4 Lecture 4: Wednesday, January 19 18 4.1 Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 Geometric Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 4.3 Augmented Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5 Homework Assignment #1 21 6 Homework Assignment #1 Solutions 22 7 Lecture 5: Friday, January 21 27 7.1 Augmented Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 7.2 Rank of a System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 7.3 Gaussian Elimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 8 Lecture 6: Monday, January 24 30 8.1 Echelon Form . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 8.2 Pivot Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 1 9 Lecture 7: Wednesday, January 26...
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This note was uploaded on 02/23/2009 for the course MA 351 taught by Professor ?? during the Spring '08 term at Purdue University-West Lafayette.

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Ma351-2005 - MA 351 Elementary Linear Algebra Purdue University Edray Herber Goins January 2005 May 2005 Contents 1 Lecture 1 Monday January 10 8

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