{"id":108,"date":"2021-06-29T11:21:26","date_gmt":"2021-06-29T11:21:26","guid":{"rendered":"https:\/\/maremathics.pfst.hr\/?p=108"},"modified":"2022-09-09T12:37:56","modified_gmt":"2022-09-09T11:37:56","slug":"3-matrices-and-determinants","status":"publish","type":"post","link":"https:\/\/maremathics.pfst.hr\/?p=108","title":{"rendered":"3. Matrices and Determinants"},"content":{"rendered":"
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Abstract<\/h4>\n\n\n\n

This chapter introduces the concept of matrix. Firstly, some operations with matrices are defined, then the determinant of the square matrix and the inverse matrix of the regular matrix. After that, it is demonstrated how to solve matrix equations and how a system of linear equations can be solved using matrices. Each topic is covered in detail, and in addition to some solved examples, it also contains exercises. At the end of the chapter is a knowledge test. Additional applications in MATLAB, Excel and Geogebra can be used to check the obtained solutions or to make faster calculations (if the procedure for solving exercises is not required).<\/p>\n\n\n\n

Aim<\/h4>\n\n\n\n

Learn how to calculate the determinant, inverse matrix and how to solve a system of linear equations using matrices.<\/p>\n\n\n\n

Learning outcomes<\/h4>\n\n\n\n
  1. Apply arithmetic operations with matrices in solving different tasks and problems,<\/li>
  2. Calculate the determinant using the basic properties of the determinant,<\/li>
  3. Determine the inverse matrix using the Gauss-Jordan method,<\/li>
  4. Solve a linear system using matrices.<\/li><\/ol>\n\n\n\n

    Previous knowledge of mathematics<\/h4>\n\n\n\n

    The student should know the basic arithmetic operations (addition, subtraction, multiplication, and division) with real numbers.<\/p>\n\n\n\n

    Applications<\/h4>\n\n\n\n

    In geometry, in processing of digital photography, model of consumer preference, encryption and decoding of messages in cryptography, analysis of an economic system, regression line with the least, square deviation from the given data set, problem of transport and distribution, traveling salesman problem…<\/p>\n\n\n\n

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    Full Text Download<\/strong><\/td>\"ENG\"<\/a><\/td>\"HR\"<\/a><\/td>\"LT\"<\/a><\/td>\"PL\"<\/a><\/td>\"\"<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
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    Contents<\/h4>\n\n\n\n
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    1. Matrix<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n\n\n\n

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    2. Matrix arithmetic<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n\n\n\n

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    3. Matrix Polynominal<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n\n\n\n

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    4. Determinant of a square matrix<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n

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    5. Determinant of the Matrix of higher order<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n\n\n\n

    <\/i><\/div>

    6. Laplace Expansion for the determinant<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n\n\n\n

    <\/i><\/div>

    7. Inverse matrix<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n\n\n\n

    <\/i><\/div>

    8. determining the inverse matrix by calculating determinants<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n

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    9. matrix equations<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n\n\n\n

    <\/i><\/div>

    10. matrix rank<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n\n\n\n

    <\/i><\/div>

    11. Systems of linear algebraic equations<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n\n\n\n

    <\/i><\/div>

    12. Some examples of matrix application<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n

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    <\/i><\/div>

    13. Exercises<\/a><\/h3><\/div>

    PDF<\/p><\/div><\/div><\/div><\/div>\n\n\n\n

    <\/div>

    Quiz – Matrices and Determinants<\/a><\/h3><\/div>

    Google Forms<\/p><\/div><\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n

    <\/div>\n\n\n\n

    <\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"

    More<\/i><\/a><\/p>\n","protected":false},"author":1,"featured_media":127,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-108","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-io-2"],"rise-blocks_total_comments":0,"rise-blocks_categories":[{"term_id":5,"name":"Intellectual Output 2 - Lessons","slug":"io-2","term_group":0,"term_taxonomy_id":5,"taxonomy":"category","description":"","parent":0,"count":9,"filter":"raw","cat_ID":5,"category_count":9,"category_description":"","cat_name":"Intellectual Output 2 - Lessons","category_nicename":"io-2","category_parent":0}],"rise-blocks_excerpt":"Abstract This chapter introduces the concept of matrix. Firstly, some operations with matrices are defined, then the determinant of the square matrix and the inverse matrix of the regular matrix. After that, it is demonstrated how to solve matrix equations and how a system of linear equations can be solved using matrices. Each topic is covered in detail, and in..","_links":{"self":[{"href":"https:\/\/maremathics.pfst.hr\/index.php?rest_route=\/wp\/v2\/posts\/108","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/maremathics.pfst.hr\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/maremathics.pfst.hr\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/maremathics.pfst.hr\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/maremathics.pfst.hr\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=108"}],"version-history":[{"count":27,"href":"https:\/\/maremathics.pfst.hr\/index.php?rest_route=\/wp\/v2\/posts\/108\/revisions"}],"predecessor-version":[{"id":4431,"href":"https:\/\/maremathics.pfst.hr\/index.php?rest_route=\/wp\/v2\/posts\/108\/revisions\/4431"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/maremathics.pfst.hr\/index.php?rest_route=\/wp\/v2\/media\/127"}],"wp:attachment":[{"href":"https:\/\/maremathics.pfst.hr\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=108"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/maremathics.pfst.hr\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=108"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/maremathics.pfst.hr\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=108"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}