Math 111 Homework 1 fall 2007 due 14/9 1. (1.2; 17) Determine the values of h such that the matrix is the augmented matrix of a system which admits a solution. 2 3 4 6 h 7 2. (1.2; 12) Find the general solutions of the system whose augmented matrix is 1 −7 0 6 5 0 0 1 −2 −3 −1 7 −4 2 7 1 −2 4 3. (1.3; 17) Let a1 = 4 ‚ a2 = −3 ‚ b = 1 . For what −2 7 h value(s) of h is b in the plane spanned by a1 and a2? 4. (1.4; 15) Let A = b1 2 −1 and b = . Show that the equation
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movements of the 1960s and increasing focus on racial equality in United States public schools‚ black females were often either misrepresented or unclassified as a distinct group. Because feminist epistemologies tend to be concerned with the education of White girls and women‚ and raced-based epistemologies tend to be consumed with the
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1.1 SOLUTIONS Notes: The key exercises are 7 (or 11 or 12)‚ 19–22‚ and 25. For brevity‚ the symbols R1‚ R2‚…‚ stand for row 1 (or equation 1)‚ row 2 (or equation 2)‚ and so on. Additional notes are at the end of the section. 1. x1 + 5 x2 = 7 −2 x1 − 7 x2 = −5 1 −2 5 −7 7 −5 x1 + 5 x2 = 7 Replace R2 by R2 + (2)R1 and obtain: 3x2 = 9 x1 + 5 x2 = 7 x2 = 3 x1 1 0 1 0 1 0 5 3 5 1 0 1 7 9 7 3 −8 3 Scale R2 by 1/3: Replace R1 by R1
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Examples in Plotting 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Matrices—Two–Dimensional Arrays 13 16.1 Size of a matrix . . . . . . . . . . . . 14 16.2 Transpose of a matrix . . . . . . . . 14 16.3 Special Matrices . . . . . . . . . . . 14 16.4 The Identity Matrix . . . . . . . . . 14 16.5 Diagonal Matrices . . . . . . . . . . 15 16.6 Building Matrices . . . . . . . . . . . 15 16.7 Tabulating Functions . . . . . . . . . 15 16.8 Extracting
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Management and Planning Tools MANAGEMENT AND PLANNING TOOLS WHY ‚WHY AFFINITY DIAGRAM INTERRELATIONSHIP DIAGRAM PRIORITIZATION MATRICES NOMINAL GROUP TECHNIQUE FORCED FIELD ANALYSIS TREE DIAGRAM PROCESS DECISION PROGRAM CHART MATRIX DIAGRAM ACTIVITY NETWORK DIAGRAM Management & Planning tools While most leaders recognize the value of good planning‚ most lack the experience and methods to do it systematically. As a result‚ group planning efforts are often frustrating‚ generating plans
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What is Panopticism and what in the world does it pertain to? These are some of the questions that I asked myself as I began to read this interesting essay by Michel Foucault. His work is central to many of the Humanities and social science parts of life. He came up with idea that people govern themselves‚ and his Panopticism essay revolves basically around this central idea. There are many panoptic examples in society today that have both positive and negative connotation. Generally I believe the
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of linear algebra or matrix theory. The introduction and development of the notation of matrix and system of linear algebra followed the development of determinant‚ which rose from the study of coefficient system of linear equations. Leibnitz‚ one of the founders of calculus used determinant in 1693 an Cramer presented his determinant - based formula system of solving linear equations (known as Cramer’s’ rule) in 1750. In 1848‚ James J Sylvester introduced the term “matrix” which was Latin word
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techniques discussed in this class in practical situations. This write-up will introduce students to the various mathematical and statistical functions available in EXCEL and explain how to use them. In section 2‚ I will discuss the various array (matrix) functions available in EXCEL that are useful for data analysis and asset allocation. I will also introduce you to the capabilities of the SOLVER function in EXCEL and take you through a hypothetical example dealing with allocating wealth efficiently
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Equation of Straight lines‚ Concept of circle‚ Equation of circle‚ finding centre and radius of circle 6 MID WEEK 7 Matrices Introduction to matrices‚ classification‚ representation‚ different forms of a matrix‚ addition‚ subtraction‚ scalar and matrix multiplication‚ transpose of matrix‚ inverse of matrix‚ solving linear equations using matrices (Cramers rule) 8 Functions Introduction to function‚ plotting graphs
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GosP’zs) 3. (t.r) lrl (i) o=lJ‚ lrrl \’/z (a) ’/z ) Describe fully the single transformation represented by the matrix A. The matrix B represents an enlargement‚ scale factor (b) Write 2‚with centre the origin. down the matrix B. (1) (iD -t = (j‚ i)‚ where k is apositive constant. Triangle Thas an area of 16 square units. Triangle 7 is transformed onto the triangle matrix M. T’ by the transformation represented by the Given that the area of the triangle T’ is 224 square units‚ find
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