real world matrix problems

Mathematics Direct citing (if referenced properly) Thank you so much for your respect to the authors copyright. $2002.50. Get Full Work (adsbygoogle = window.adsbygoogle || []).push({}); Disclaimer: Using this Service/Resources: You are allowed to use the original model papers you will receive in the following ways: 1. We've received widespread press coverage since 2003, Your UKEssays purchase is secure and we're rated 4.4/5 on reviews.co.uk. For e.g. *You can also browse our support articles here >. Historically, the early emphasis was on the determinant, not the matrix. l m � � � � � � � � � � � � � ��帧��噈��|�mbTCm�!j�6 h�P4 heB� EH��OJ QJ UjP$�N Matrices are also used in representing the real world data’s like the population of people, infant mortality rate, etc. [latex]A=\left[\begin{array}{cc}4& 1\\ 3& 2\end{array}\right]\text{ and }B=\left[\begin{array}{cc}5& 9\\ 0& 7\end{array}\right][/latex]. h�P4 h�:� UV!j� h�P4 h�:� EH��OJ QJ Uj �N Preview. We refer to m and n as the dimensions of the matrix. Real World Word Problems. Whereas in programming which is taught at the university, matrices and inverse matrices are used for coding and encrypting messages. They have the tools and resources. If the inner dimensions do not match, the product is not defined. h�P4 h;$� UV!j�. They estimate that 15% more equipment is needed in both labs. To obtain the entry in row 1, column 2 of [latex]AB,\text{}[/latex] multiply the first row of [latex]A[/latex] by the second column in [latex]B[/latex] and add. 1d. EMBED Equation.DSMT4 1c. Matrices are fundamental to resource allocation problems - like working out how much of a particular type of product a factory should produce, or how to set pricing for different products. The origin of mathematical matrices lies with the study of simultaneous linear equations. A matrix is often referred to by its size or dimensions: [latex]\text{ }m\text{ }\times \text{ }n\text{ }[/latex] indicating [latex]m[/latex] rows and [latex]n[/latex] columns. In schools for e.g. 8b. Regressions can be used in business to evaluate trends and make estimates. 2a. Our academic experts are ready and waiting to assist with any writing project you may have. Finding a greatest common factor won't do anything about global famine, world hunger or whatever relationship troubles you may find yourself in in the future. In industries and businesses it is crucial to be fast and accurate in decision making. For example, three matrices named A,B,A,B, and CCare shown below. This illustrates the fact that matrix multiplication is not commutative. 3. That rather depends on what you mean by "real life". ��ࡱ� > �� ~ �� a �� 9 bjbj*�*� 4 H�=bH�=b9 �� 4 � � � � � � � � � _ _ _ u w w w w w w $ 2 � � � � � _ _ _ _ _ � � � � � � � _ h�P4 h;$� EH��OJ QJ Uj�"�N He gave a precise explanation of an inverse of a matrix. In matrix [latex]A[/latex] shown below, the entry in row 2, column 3 is [latex]{a}_{23}[/latex]. In other words, row 2 of [latex]A[/latex] times column 1 of [latex]B[/latex]; row 2 of [latex]A[/latex] times column 2 of [latex]B[/latex]; row 2 of [latex]A[/latex] times column 3 of [latex]B[/latex]. Matrices are often referred to by their dimensions: [latex]m\times n[/latex] indicating [latex]m[/latex] rows and [latex]n[/latex] columns. + , n o p q � � � � � � � For example, three matrices named [latex]A,B,\text{}[/latex] and [latex]C[/latex] are shown below. Enter the operation into the calculator, calling up each matrix variable as needed. � As the dimensions of [latex]A[/latex] are [latex]2\text{}\times \text{}3[/latex] and the dimensions of [latex]B[/latex] are [latex]3\text{}\times \text{}2,\text{}[/latex] these matrices can be multiplied together because the number of columns in [latex]A[/latex] matches the number of rows in [latex]B[/latex]. 2b. No plagiarism, guaranteed! The dimensions of [latex]B[/latex] are [latex]3\times 2[/latex] and the dimensions of [latex]A[/latex] are [latex]2\times 3[/latex]. In a video game, this would render the upside-down mirror image of an assassin reflected in a pond of blood. 2. Matrices provide a theoretically and practically useful way of approaching many types of problems including; Solutions of system of linear equations, Equilibrium of rigid bodies, Graph theory, Theory of games, Leontief economics model, Forest management, Computer graphics and Computed tomography, Genetics, Cryptography, Electrical networks, etc. For example, time, temperature, and distance are scalar quantities. We can add or subtract a [latex]\text{ }3\text{ }\times \text{ }3\text{ }[/latex] matrix and another [latex]\text{ }3\text{ }\times \text{ }3\text{ }[/latex] matrix, but we cannot add or subtract a [latex]\text{ }2\text{ }\times \text{ }3\text{ }[/latex] matrix and a [latex]\text{ }3\text{ }\times \text{ }3\text{ }[/latex] matrix because some entries in one matrix will not have a corresponding entry in the other matrix. 9. In physics related applications, matrices are used in the study of electrical circuits, quantum mechanics and optics. � [latex]A=\left[\begin{array}{l}\begin{array}{ccc}-1& 2& 3\end{array}\hfill \\ \begin{array}{ccc}4& 0& 5\end{array}\hfill \end{array}\right]\text{ and }B=\left[\begin{array}{c}5\\ -4\\ 2\end{array}\begin{array}{c}-1\\ 0\\ 3\end{array}\right][/latex]. When complete, the product matrix will be, [latex]AB=\left[\begin{array}{c}\begin{array}{l}{a}_{11}\cdot {b}_{11}+{a}_{12}\cdot {b}_{21}+{a}_{13}\cdot {b}_{31}\\ \end{array}\\ {a}_{21}\cdot {b}_{11}+{a}_{22}\cdot {b}_{21}+{a}_{23}\cdot {b}_{31}\end{array}\begin{array}{c}\begin{array}{l}{a}_{11}\cdot {b}_{12}+{a}_{12}\cdot {b}_{22}+{a}_{13}\cdot {b}_{32}\\ \end{array}\\ {a}_{21}\cdot {b}_{12}+{a}_{22}\cdot {b}_{22}+{a}_{23}\cdot {b}_{32}\end{array}\begin{array}{c}\begin{array}{l}{a}_{11}\cdot {b}_{13}+{a}_{12}\cdot {b}_{23}+{a}_{13}\cdot {b}_{33}\\ \end{array}\\ {a}_{21}\cdot {b}_{13}+{a}_{22}\cdot {b}_{23}+{a}_{23}\cdot {b}_{33}\end{array}\right][/latex]. EMBED Equation.DSMT4 14. h�P4 h�:� UV!j.$ h�P4 h�:� EH��OJ QJ Uj� �N In fact it is in front of us every day when going to work, at the university and even at home. Continue the pattern until all entries have been added. 10. The calculator gives us the following matrix. Matrices and determinants were discovered and developed in the 18th and 19th centuries. First, find [latex]3A,\text{}[/latex] then [latex]2B[/latex]. A goal costs $300; a ball costs $10; and a jersey costs $30. Copyright © 2003 - 2020 - UKEssays is a trading name of All Answers Ltd, a company registered in England and Wales. Many real-world problems can often be solved using matrices. Indeed, it is fair to say that the nine chapters’ text on Mathematical Art written during the Han Dynasty gives the first known example of matrix methods. APPLICATION OF MATRICES TO REAL LIFE PROBLEMS CHAPTER ONE INTRODUCTION AND LITERATURE REVIEW INTRODUCTION Matrices and determinants were discovered and developed in the 18th and 19th centuries. We are here to answer your questions. As a source for ideas for your own research work (if properly referenced). In hospitals, medical imaging, CAT scans and MRI’s, use matrices to operate. Application of Regression in real-life problems. You can view samples of our professional work here. They are 0�s as they describe the distance from A to A, for example. We perform matrix multiplication to obtain costs for the equipment. [latex]A=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right],B=\left[\begin{array}{ccc}1& 2& 7\\ 0& -5& 6\\ 7& 8& 2\end{array}\right],C=\left[\begin{array}{c}-1\\ 0\\ 3\end{array}\begin{array}{c}3\\ 2\\ 1\end{array}\right][/latex]. EMBED Equation.DSMT4 3. [latex]A=\left[\begin{array}{rrr}\hfill -15& \hfill 25& \hfill 32\\ \hfill 41& \hfill -7& \hfill -28\\ \hfill 10& \hfill 34& \hfill -2\end{array}\right],B=\left[\begin{array}{rrr}\hfill 45& \hfill 21& \hfill -37\\ \hfill -24& \hfill 52& \hfill 19\\ \hfill 6& \hfill -48& \hfill -31\end{array}\right],\text{and }C=\left[\begin{array}{rrr}\hfill -100& \hfill -89& \hfill -98\\ \hfill 25& \hfill -56& \hfill 74\\ \hfill -67& \hfill 42& \hfill -75\end{array}\right][/latex].