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Boundless Lecture Slides

Boundless Lecture Slides. Available on the Boundless Teaching Platform. Free to share, print, make copies and changes. Get yours at www.boundless.com. Using Boundless Presentations. Boundless Teaching Platform

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Boundless Lecture Slides

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  1. Boundless Lecture Slides Available on the Boundless Teaching Platform Free to share, print, make copies and changes. Get yours at www.boundless.com

  2. Using Boundless Presentations Boundless Teaching Platform Boundless empowers educators to engage their students with affordable, customizable textbooks and intuitive teaching tools. The free Boundless Teaching Platform gives educators the ability to customize textbooks in more than 20 subjects that align to hundreds of popular titles. Get started by using high quality Boundless books, or make switching to our platform easier by building from Boundless content pre-organized to match the assigned textbook. This platform gives educators the tools they need to assign readings and assessments, monitor student activity, and lead their classes with pre-made teaching resources. Get started now at: • The Appendix The appendix is for you to use to add depth and breadth to your lectures. You can simply drag and drop slides from the appendix into the main presentation to make for a richer lecture experience. http://boundless.com/teaching-platform • Free to edit, share, and copy Feel free to edit, share, and make as many copies of the Boundless presentations as you like. We encourage you to take these presentations and make them your own. If you have any questions or problems please email: educators@boundless.com Free to share, print, make copies and changes. Get yours at www.boundless.com

  3. About Boundless • Boundless is an innovative technology company making education more affordable and accessible for students everywhere. The company creates the world’s best open educational content in 20+ subjects that align to more than 1,000 popular college textbooks. Boundless integrates learning technology into all its premium books to help students study more efficiently at a fraction of the cost of traditional textbooks. The company also empowers educators to engage their students more effectively through customizable books and intuitive teaching tools as part of the Boundless Teaching Platform. More than 2 million learners access Boundless free and premium content each month across the company’s wide distribution platforms, including its website, iOS apps, Kindle books, and iBooks. To get started learning or teaching with Boundless, visit boundless.com. Free to share, print, make copies and changes. Get yours at www.boundless.com

  4. Introduction to Matrices Matrices Using Matrices to Solve Systems of Equations Inverses of Matrices Determinants and Cramer's Rule ] Matrices Free to share, print, make copies and changes. Get yours at www.boundless.com

  5. Matrices > Introduction to Matrices Introduction to Matrices • What is a Matrix? • Addition and Subtraction; Scalar Multiplication • Matrix Multiplication • The Identity Matrix Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/matrices-340/introduction-to-matrices-358/

  6. Matrices > Using Matrices to Solve Systems of Equations Using Matrices to Solve Systems of Equations • Matrix Equations • Matrices and Row Operations • Simplifying Matrices With Row Operations Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/matrices-340/using-matrices-to-solve-systems-of-equations-359/

  7. Matrices > Inverses of Matrices Inverses of Matrices • The Inverse of a Matrix • Solving Systems of Equations Using Matrix Inverses Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/matrices-340/inverses-of-matrices-360/

  8. Matrices > Determinants and Cramer's Rule Determinants and Cramer's Rule • Determinants of 2-by-2 Square Matrices • Cofactors, Minors, and Further Determinants • Cramer's Rule Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/matrices-340/determinants-and-cramer-s-rule-361/

  9. Appendix Free to share, print, make copies and changes. Get yours at www.boundless.com

  10. Matrices Key terms • augmented matrixA matrix obtained by appending the columns of two given matrices, usually for the purpose of performing the same elementary row operations on each of the given matrices. • cofactorThe signed minor of an entry of a matrix. • column vectorA matrix with a single column • determinantThe unique scalar function over square matrices which is distributive over matrix multiplication, multilinear in the rows and columns, and takes the value of 1 for the unit matrix. Its abbreviation is "". • determinantThe unique scalar function over square matrices which is distributive over matrix multiplication, multilinear in the rows and columns, and takes the value of for the unit matrix. Its abbreviation is "". • elementAn individual item in a matrix • identity matrixA diagonal matrix all of the diagonal elements of which are equal to , the rest being equal to . • identity matrixA diagonal matrix all of the diagonal elements of which are equal to , the rest being equal to . • inverse matrixA square matrix  with an associated matrix such that multiplied by and multiplied by both equal the identity matrix. • inverse matrixFor a matrix , if a matrix  exist such that multiplied by and multiplied by both equal the identity matrix, then  is the inverse of . • linear equationA polynomial equation of the first degree (such as ). • matrixA rectangular arrangement of numbers or terms having various uses such as transforming coordinates in geometry, solving systems of linear equations in linear algebra and representing graphs in graph theory. Free to share, print, make copies and changes. Get yours at www.boundless.com

  11. Matrices • matrixA rectangular arrangement of numbers or terms having various uses such as transforming coordinates in geometry, solving systems of linear equations in linear algebra and representing graphs in graph theory. • matrixA rectangular arrangement of numbers or terms having various uses such as transforming coordinates in geometry, solving systems of linear equations in linear algebra and representing graphs in graph theory. • matrixA rectangular arrangement of numbers or terms having various uses such as transforming coordinates in geometry, solving systems of linear equations in linear algebra and representing graphs in graph theory. • matrixA rectangular array of numbers, symbols, or expressions, arranged in rows and columns • minorThe determinant of some smaller square matrix, cut down from matrix by removing one or more of its rows or columns. • row equivalentIn linear algebra, when one matrix can be changed to the other by a sequence of elementary row operations. • row spaceThe set of all possible linear combinations of its row vectors. • row vectorA matrix with a single row • scalarA quantity that has magnitude but not direction. • singular matrixA matrix that has no inverse. • square matrixA matrix which has the same number of rows and columns • square matrixA matrix having the same number of rows as columns. Free to share, print, make copies and changes. Get yours at www.boundless.com

  12. Matrices Matrix Multiplication This figure illustrates diagrammatically the product of two matrices A and B, showing how each intersection in the product matrix corresponds to a row of A and a column of B. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."Matrix multiplication."GNU FDLhttp://en.wikipedia.org/wiki/Matrix_multiplication%23Matrix_product_.28two_matrices.29View on Boundless.com

  13. Matrices Matrix Dimensions Each element of a matrix is often denoted by a variable with two subscripts. For instance,  represents the element at the second row and first column of a matrix A. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia."247px-Matrix.svg.png."CC BY-SA 3.0https://en.wikipedia.org/wiki/Matrix_(mathematics)View on Boundless.com

  14. Matrices Attribution • Wiktionary."linear equation."CC BY-SA 3.0http://en.wiktionary.org/wiki/linear_equation • Wiktionary."inverse matrix."CC BY-SA 3.0http://en.wiktionary.org/wiki/inverse_matrix • OpenStax CNX."Kenny Felder, Advanced Algebra II: Conceptual Explanations. September 17, 2013."CC BY 3.0http://cnx.org/content/m18292/latest/?collection=col10624 • Wikipedia."minor."CC BY-SA 3.0http://en.wikipedia.org/wiki/minor • Wikipedia."Minor (linear algebra)."CC BY-SA 3.0http://en.wikipedia.org/wiki/Minor_(linear_algebra) • Wikipedia."Cofactor (linear algebra)."CC BY-SA 3.0http://en.wikipedia.org/wiki/Cofactor_(linear_algebra) • Wiktionary."cofactor."CC BY-SA 3.0http://en.wiktionary.org/wiki/cofactor • Wikipedia."Determinant."CC BY-SA 3.0http://en.wikipedia.org/wiki/Determinant • Wiktionary."determinant."CC BY-SA 3.0http://en.wiktionary.org/wiki/determinant • Wikipedia."augmented matrix."CC BY-SA 3.0http://en.wikipedia.org/wiki/augmented%20matrix • Wikipedia."Gaussian elimination."CC BY-SA 3.0http://en.wikipedia.org/wiki/Gaussian_elimination • Wikipedia."Elementary row operations."CC BY-SA 3.0http://en.wikipedia.org/wiki/Elementary_row_operations • Wikipedia."Triangular matrix."CC BY-SA 3.0http://en.wikipedia.org/wiki/Triangular_matrix • Wikipedia."System of linear equations."CC BY-SA 3.0http://en.wikipedia.org/wiki/System_of_linear_equations • Wikipedia."Augmented matrix."CC BY-SA 3.0http://en.wikipedia.org/wiki/Augmented_matrix • Wikipedia."Row echelon form."CC BY-SA 3.0http://en.wikipedia.org/wiki/Row_echelon_form • OpenStax CNX."Doug Daniels and Steven Cox, Row Reduced Form. September 17, 2013."CC BY 3.0http://cnx.org/content/m10295/latest/ Free to share, print, make copies and changes. Get yours at www.boundless.com

  15. Matrices • Wikipedia."Identity matrix."CC BY-SA 3.0http://en.wikipedia.org/wiki/Identity_matrix • Wiktionary."identity matrix."CC BY-SA 3.0http://en.wiktionary.org/wiki/identity_matrix • OpenStax CNX."Kenny Felder, Advanced Algebra II: Conceptual Explanations. September 17, 2013."CC BY 3.0http://cnx.org/content/m18291/latest/?collection=col10624 • Wiktionary."matrix."CC BY-SA 3.0http://en.wiktionary.org/wiki/matrix • OpenStax CNX."Kenny Felder, Advanced Algebra II: Conceptual Explanations. September 17, 2013."CC BY 3.0http://cnx.org/content/m18293/latest/?collection=col10624 • Wikipedia."Inverse matrix."CC BY-SA 3.0http://en.wikipedia.org/wiki/Inverse_matrix • Wiktionary."inverse matrix."CC BY-SA 3.0http://en.wiktionary.org/wiki/inverse_matrix • Wiktionary."identity matrix."CC BY-SA 3.0http://en.wiktionary.org/wiki/identity_matrix • OpenStax CNX."Kenny Felder, Advanced Algebra II: Conceptual Explanations. September 17, 2013."CC BY 3.0http://cnx.org/content/m18294/latest/?collection=col10624 • Wiktionary."matrix."CC BY-SA 3.0http://en.wiktionary.org/wiki/matrix • Wikipedia."System of linear equations."CC BY-SA 3.0http://en.wikipedia.org/wiki/System_of_linear_equations%23Matrix_equation • Wikipedia."Matrix equation."CC BY-SA 3.0http://en.wikipedia.org/wiki/Matrix_equation • Wikipedia."System of linear equations."CC BY-SA 3.0http://en.wikipedia.org/wiki/System_of_linear_equations%23Matrix_solution • Openstax."Solving Systems with Inverses."CC BY-SA 3.0http://cnx.org/contents/mwjClAV_@3.314:Y00jh3Qp@6/Solving-Systems-with-Inverses • Wiktionary."matrix."CC BY-SA 3.0http://en.wiktionary.org/wiki/matrix • Wikipedia."Determinant."CC BY-SA 3.0http://en.wikipedia.org/wiki/Determinant • Wikipedia."Cramer's rule."CC BY-SA 3.0http://en.wikipedia.org/wiki/Cramer's_rule • Wiktionary."determinant."CC BY-SA 3.0http://en.wiktionary.org/wiki/determinant • Wiktionary."square matrix."CC BY-SA 3.0http://en.wiktionary.org/wiki/square_matrix Free to share, print, make copies and changes. Get yours at www.boundless.com

  16. Matrices • Wikipedia."Matrix (mathematics)."CC BY-SA 3.0http://en.wikipedia.org/wiki/Matrix_(mathematics) • Wikipedia."row equivalent."CC BY-SA 3.0http://en.wikipedia.org/wiki/row%20equivalent • Wikipedia."Row equivalence."CC BY-SA 3.0http://en.wikipedia.org/wiki/Row_equivalence • Wikipedia."system of linear equations."CC BY-SA 3.0https://en.wikipedia.org/wiki/System_of_linear_equations • Wikipedia."Matrix (mathematics)."CC BY-SA 3.0http://en.wikipedia.org/wiki/Matrix_(mathematics) • Wikipedia."Scalar multiplication."CC BY-SA 3.0http://en.wikipedia.org/wiki/Scalar_multiplication • Wiktionary."scalar."CC BY-SA 3.0http://en.wiktionary.org/wiki/scalar • Openstax."Adding and Subtracting Matricies."CC BY-SA 3.0http://cnx.org/contents/mwjClAV_@3.314:UIpNTgE2@3/Matrices-and-Matrix-Operations • OpenStax CNX."Kenny Felder, Matrix Concepts -- Explanations. September 18, 2013."CC BY 3.0http://cnx.org/content/m18311/latest/ • ck12."Adding and Subtracting Real Life Problems."CC BYhttps://braingenie.ck12.org/skills/106769 • Wikipedia."Matrix (mathematics)."CC BY-SA 3.0http://en.wikipedia.org/wiki/Matrix_(mathematics) • Wikipedia."Matrix multiplication."CC BY-SA 3.0http://en.wikipedia.org/wiki/Matrix_multiplication%23Matrix_product_.28two_matrices.29 • Wiktionary."matrix."CC BY-SA 3.0http://en.wiktionary.org/wiki/matrix • OpenStax CNX."Kenny Felder, Matrix Concepts -- Multiplying Matricies. September 18, 2013."CC BY 3.0http://cnx.org/content/m18291/latest/ • Wikipedia."Matrix Dimensions."CC BY-SA 3.0https://en.wikipedia.org/wiki/Matrix_(mathematics) Free to share, print, make copies and changes. Get yours at www.boundless.com

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