![]() ![]() Therefore, the equations have no solution. Display equation 2 in the row picture (i.e. Using the row picture explain why the equations have no solu- tion. ![]() Similarly, using the column picture, explain why equation 2 has no solution. You may draw the diagrams by hand or by using drawing software such as Geogebra. ![]() (d) By using Gaussian elimination, find the inverse of the coefficient ma- trix in equation 1, part a. Simultaneous equations with infinitely many solutions. (a) Consider the equations: *+ 2y = 1 (3) 2r + 4y = 2 i. Show that the RREF of equation 3 is (630) We therefore have 0x + Oy = 0 = 0 = 0. We can only conclude that there are infinitely many solutions that satisfy r + 2y = 1. Using this, explain why there are many soutions. Using the solutions (1.0) and (-1,1) draw the column picture of 3. Usually, we set one of the variables equal to a real parameter. Write the augmented matrix for these equations and through Gaussian elimination, bring it to reduced row echelon form. Again, this gives us no useful information. Therefore, we have two equations in three variables and ii. In the row picture, each of the equations in equation 4 represents a plane. Explain the relationship between the planes described by the second and third equations in 4. You do not have to draw anything for this part iii. #Geogebra classic rref how to#Īllenby and Alan Slomson, How to Count: An Introduction to Combinatorics, Third Edition Donald Bindner and Martin Erickson, A Student’s Guide to the Study, Practice, and Tools of Modern Mathematics Juergen Bierbrauer, Introduction to Coding Theory Francine Blanchet-Sadri, Algorithmic Combinatorics on Partial Words Richard A.Pick any two solutions to 4 and draw the column picture, using either a pencil or drawing software. Brualdi and Drago˘s Cvetkovi´c, A Combinatorial Approach to Matrix Theory and Its Applications Kun-Mao Chao and Bang Ye Wu, Spanning Trees and Optimization Problems Charalambos A. Charalambides, Enumerative Combinatorics Gary Chartrand and Ping Zhang, Chromatic Graph Theory Henri Cohen, Gerhard Frey, et al., Handbook of Elliptic and Hyperelliptic Curve Cryptography Charles J. Dinitz, Handbook of Combinatorial Designs, Second Edition Martin Erickson, Pearls of Discrete Mathematics Martin Erickson and Anthony Vazzana, Introduction to Number Theory Steven Furino, Ying Miao, and Jianxing Yin, Frames and Resolvable Designs: Uses, Constructions, and Existence Mark S. Gockenbach, Finite-Dimensional Linear Algebra Randy Goldberg and Lance Riek, A Practical Handbook of Speech Coders Jacob E. Goodman and Joseph O’Rourke, Handbook of Discrete and Computational Geometry, Second Edition Jonathan L. Gross, Combinatorial Methods with Computer Applications Jonathan L. Gross and Jay Yellen, Graph Theory and Its Applications, Second Edition Jonathan L. Gross and Jay Yellen, Handbook of Graph Theory David S. Gunderson, Handbook of Mathematical Induction: Theory and Applications Darrel R. Walker, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition Johnson, Introduction to Information Theory and Data Compression, Second Edition Darel W. Devitt, Network Reliability: Experiments with a Symbolic Algebra Environment Silvia Heubach and Toufik Mansour, Combinatorics of Compositions and Words Leslie Hogben, Handbook of Linear Algebra Derek F. O’Brien, Handbook of Computational Group Theory David M. Visentin, An Atlas of Smaller Maps in Orientable and Nonorientable Surfaces Richard E. Stitzinger, Applications of Abstract Algebra with Maple™ and MATLAB®, Second Edition Patrick Knupp and Kambiz Salari, Verification of Computer Codes in Computational Science and Engineering William Kocay and Donald L. Kreher, Graphs, Algorithms, and Optimization Donald L. Stinson, Combinatorial Algorithms: Generation Enumeration and Search C. Rodger, Design Theory, Second Edition Hang T. Lau, A Java Library of Graph Algorithms and Optimization Elliott Mendelson, Introduction to Mathematical Logic, Fifth Edition Alfred J. Vanstone, Handbook of Applied Cryptography Richard A. Mollin, Advanced Number Theory with Applications Richard A. Mollin, Algebraic Number Theory Richard A. Mollin, Codes: The Guide to Secrecy from Ancient to Modern Times Richard A. Mollin, Fundamental Number Theory with Applications, Second Edition Richard A. Mollin, An Introduction to Cryptography, Second Edition Richard A. Mollin, RSA and Public-Key Cryptography Carlos J. Wagstaff, Jr., Sums of Squares of Integers Dingyi Pei, Authentication Codes and Combinatorial Designs Kenneth H. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |