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4. Addition and Subtraction; Scalar Multiplication Matrix Multiplication Matrix Equations Matrix Operations Systems of Equations and Matrices > Matrix Operations Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra?campaign_content=book_196_section_44&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=dir ect&utm_source=boundless

5. When performing addition, you add each number in the first matrix to the corresponding number in the second matrix. When performing subtraction, simply subtract a number in one of the matrices from the corresponding number in the other matrix. Addition and subtraction require that the matrices be the same dimensions. Also, you must begin and end with the same dimensions. Scalar multiplication of a real Euclidean vector by a positive real number multiplies the magnitude of the vector without changing its direction. Addition and Subtraction; Scalar Multiplication Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/systems-of-equations-and-matrices-6/matrix-operations-44/addition-and- subtraction-scalar-multiplication-200- 11209?campaign_content=book_196_section_44&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boun dless Scalar Multiplication View on Boundless.com Systems of Equations and Matrices > Matrix Operations

6. If A is an n×m matrix and B is an m×p matrix, the result AB of their multiplication is an n×p matrix defined only if the number of columns m in A is equal to the number of rows m in B. Treating the rows and columns in each matrix as row and column vectors respectively, this entry is also their vector dot product. The product of a square matrix multiplied by a column matrix arises naturally in linear algebra for solving linear equations and representing linear transformations. Matrix Multiplication Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/systems-of-equations-and-matrices-6/matrix-operations-44/matrix- multiplication-201- 11210?campaign_content=book_196_section_44&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boun dless Matrix Multiplication View on Boundless.com Systems of Equations and Matrices > Matrix Operations

7. If A is an m-by-n matrix, x designates a column vector (i.e., n×1-matrix) of n variables x1, x2,..., xn, and b is an m×1-column vector, then the matrix equation: [Equation 1]. Matrix Equations Systems of Equations and Matrices > Matrix Operations Free to share, print, make copies and changes. Get yours at www.boundless.com www.boundless.com/algebra/textbooks/boundless-algebra-textbook/systems-of-equations-and-matrices-6/matrix-operations-44/matrix-equations- 202- 11088?campaign_content=book_196_section_44&campaign_term=Algebra&utm_campaign=powerpoint&utm_medium=direct&utm_source=boun dless Equation 1 View on Boundless.com Matrix equation View on Boundless.com

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

9. Key terms matrix A 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. scalar A quantity that has magnitude but not direction; compare vector Free to share, print, make copies and changes. Get yours at www.boundless.com Systems of Equations and Matrices

10. Matrix equation The vector equation is equivalent to a matrix equation of the form: Ax=b, where A is an m×n matrix, x is a column vector with n entries, and b is a column vector with m entries. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "System of linear equations." GNU FDL http://en.wikipedia.org/wiki/System_of_linear_equations#Matrix_equation View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/System_of_linear_equations#Matrix_equationView on Boundless.com Systems of Equations and Matrices

11. 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 FDL http://en.wikipedia.org/wiki/Matrix_multiplication#Matrix_product_.28two_matrices.29 View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Matrix_multiplication#Matrix_product_.28two_matrices.29View on Boundless.com Systems of Equations and Matrices

12. Scalar Multiplication Scalar multiplication has the above properties. Free to share, print, make copies and changes. Get yours at www.boundless.com Wikipedia. "Scalar multiplication." GNU FDL http://en.wikipedia.org/wiki/Scalar_multiplication View on Boundless.comGNU FDLhttp://en.wikipedia.org/wiki/Scalar_multiplicationView on Boundless.com Systems of Equations and Matrices

13. Free to share, print, make copies and changes. Get yours at www.boundless.com Systems of Equations and Matrices Which of the following represents a solution for the following system: x+y+z=6, 2y+5z=-4, 2x+5y-z=27? A) x=-2, y=5, z=3 B) x=1, y=2, z=3 C) x=5, y=3, z=-2 D) x=0, y=3, z=-2

14. Free to share, print, make copies and changes. Get yours at www.boundless.comwww.boundless.com Boundless - LO. "Boundless." CC BY-SA 3.0 http://www.boundless.com/CC BY-SA 3.0http://www.boundless.com/ Systems of Equations and Matrices Which of the following represents a solution for the following system: x+y+z=6, 2y+5z=-4, 2x+5y-z=27? A) x=-2, y=5, z=3 B) x=1, y=2, z=3 C) x=5, y=3, z=-2 D) x=0, y=3, z=-2

15. Attribution Wikipedia. "Matrix equation." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Matrix_equationCC BY-SA 3.0http://en.wikipedia.org/wiki/Matrix_equation Wikipedia. "System of linear equations." CC BY-SA 3.0 http://en.wikipedia.org/wiki/System_of_linear_equations#Matrix_equationCC BY-SA 3.0 http://en.wikipedia.org/wiki/System_of_linear_equations#Matrix_equation Wikipedia. "System of linear equations." CC BY-SA 3.0 http://en.wikipedia.org/wiki/System_of_linear_equations#Matrix_solutionCC BY-SA 3.0 http://en.wikipedia.org/wiki/System_of_linear_equations#Matrix_solution Wiktionary. "matrix." CC BY-SA 3.0 http://en.wiktionary.org/wiki/matrixCC BY-SA 3.0http://en.wiktionary.org/wiki/matrix Connexions. "Matrix Concepts -- Explanations." CC BY 3.0 http://cnx.org/content/m18311/latest/CC BY 3.0http://cnx.org/content/m18311/latest/ Wikipedia. "Matrix (mathematics)." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Matrix_(mathematics)CC BY-SA 3.0http://en.wikipedia.org/wiki/Matrix_(mathematics) Wikipedia. "Scalar multiplication." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Scalar_multiplicationCC BY-SA 3.0http://en.wikipedia.org/wiki/Scalar_multiplication Wiktionary. "scalar." CC BY-SA 3.0 http://en.wiktionary.org/wiki/scalarCC BY-SA 3.0http://en.wiktionary.org/wiki/scalar Connexions. "Matrix Concepts -- Multiplying Matrices." CC BY 3.0 http://cnx.org/content/m18291/latest/CC BY 3.0http://cnx.org/content/m18291/latest/ Wikipedia. "Matrix (mathematics)." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Matrix_(mathematics)CC BY-SA 3.0http://en.wikipedia.org/wiki/Matrix_(mathematics) Wikipedia. "Matrix multiplication." CC BY-SA 3.0 http://en.wikipedia.org/wiki/Matrix_multiplication#Matrix_product_.28two_matrices.29CC BY-SA 3.0 http://en.wikipedia.org/wiki/Matrix_multiplication#Matrix_product_.28two_matrices.29 Wiktionary. "matrix." CC BY-SA 3.0 http://en.wiktionary.org/wiki/matrixCC BY-SA 3.0http://en.wiktionary.org/wiki/matrix Free to share, print, make copies and changes. Get yours at www.boundless.com Systems of Equations and Matrices