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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and classes Key OpenCV Classes Point_ Point3_ Size_ Vec Matx Scalar Rect Range Mat SparseMat Ptr Template 2D point class Template 3D point class Template size (width‚ height) class Template short vector class Template small matrix class 4-element vector Rectangle Integer value range 2D or multi-dimensional dense array (can be used to store matrices‚ images‚ histograms‚ feature descriptors‚ voxel volumes etc.) Multi-dimensional sparse array Template smart pointer class
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movies in the 1980s and1990s. Virtual Reality received mainstream attention after the release of the movie Tron in 1982‚ Star Trek the Next Generation in 1987‚ and The Matrix in 1999.Virtual reality became a reclusive subject in the mid-2000s after the end of the Matrix movie and it went into more practical uses. After the end of The Matrix movies phenomenon in 2003‚ VR quietly
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