Mathematical Analysis (Honors)
Unit 2: Matrices
In this unit, students are introduced to matrices. They use a matrix to represent and manipulate real world data using matrix addition and subtraction, matrices products, and multiplication of matrices by scalars. Students develop an understanding of how multiplication of a matrix results in a transformation of the points in the coordinate plane. Students examine 3x3 matrices in order to find the determinant. Students will see that a system of linear equations can be represented and solved algebraically as a matrix equation and the results may be verified with technology.
Students build on their work with quadratic and absolute value functions and extend their repertoire of functions to begin to explore other function families. Students discover the connections between changes in algebraic equations and transformations in the corresponding graphs. Students compare properties of two functions using multiple representations, such as, a graph, table of values, and verbal descriptions. Students begin to fit realworld data and scenarios to potential function families. This unit serves as an introduction to function families, transformations, and modeling and lays the groundwork for deeper study of individual function families.
Students build on their work with quadratic and absolute value functions and extend their repertoire of functions to begin to explore other function families. Students discover the connections between changes in algebraic equations and transformations in the corresponding graphs. Students compare properties of two functions using multiple representations, such as, a graph, table of values, and verbal descriptions. Students begin to fit realworld data and scenarios to potential function families. This unit serves as an introduction to function families, transformations, and modeling and lays the groundwork for deeper study of individual function families.
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Students will:
Perform operations on matrices and use matrices in applications.
N.VM.C.6
Use matrices to represent and manipulate data.
N.VM.C.7
Multiply matrices by scalars to produce new matrices.
N.VM.C.8
Add, subtract, and multiply matrices of appropriate dimensions.
N.VM.C.9
Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
N.VM.C.12
Work with 2x2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
Apply understanding of matrices to solve systems of equations.
PC.MA.1
Find determinants of matrices and use the determinant to determine whether the matrix has a multiplicative inverse.
Solve systems of equations.
A.REI.C.8
Model realworld data with functions. Justify why the model is most appropriate for the problem situation.
Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimensions 3x3 or greater).
Perform operations on matrices and use matrices in applications.
N.VM.C.6
Use matrices to represent and manipulate data.
 Background Info.
 Check for Understanding: Matrix Dimensions  Matrix Elements  Represent linear systems with matrices
 Review/Rewind: Intro to Matrices  Represent linear systems with matrices
N.VM.C.7
Multiply matrices by scalars to produce new matrices.
 Background Info.
 Check for Understanding: Multiply Matrix by a Scalar  Matrix Equations: Scalar Multiplication
 Review/Rewind: Multiplying by a Scalar
N.VM.C.8
Add, subtract, and multiply matrices of appropriate dimensions.
 Background Info.
 Check for Understanding: Adding and Subtracting Matrices  Adding and Subtracting Matrix Equations
 Review/Rewind: Adding and Subtracting Matrices
N.VM.C.9
Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
 Background Info.
 Check for Understanding: Multiplying Matrices
 Review/Rewind: Intro to Matrix Multiplication  Multiplying Matrices  Intro to the Identity Matrix  Zero Matrix and Matrix Multiplication  Is Matrix Multiplication Commutative?  Associative Property of Matrix Multiplication
N.VM.C.12
Work with 2x2 matrices as transformations of the plane, and interpret the absolute value of the determinant in terms of area.
 Background Info.
 Check for Understanding: Matrices as Transformations  Determinant of 2x2 Matrices
 Review/Rewind:: Transforming Vectors using Matrices  Visual Representations of Matrix Transformations  Determinant of 2x2 Matrices
Apply understanding of matrices to solve systems of equations.
PC.MA.1
Find determinants of matrices and use the determinant to determine whether the matrix has a multiplicative inverse.
 Check for Understanding: Determinant of 2x2 Matrices  Determinant of 3x3 Matrices  Inverse of 2x2 Matrix  Inverse of 3x3 Matrix
 Review/Rewind: Determinant of 2x2 Matrices  Determinant of 3x3 Matrix  Determinant of 3x3 Matrix (Shortcut)  Inverting 2x2 Matrices  Inverting 3x3 Matrices Part 1  Part 2
Solve systems of equations.
A.REI.C.8
Model realworld data with functions. Justify why the model is most appropriate for the problem situation.
 Check for Understanding: Represent Linear Systems with Matrix Equations
 Review/Rewind: Representing Linear Systems with Matrix Equations
Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimensions 3x3 or greater).
 Review/Rewind: Matrix Word Problem: Vector Combination  Matrix Word Problem:Prices
What are some signs of student mastery?

Tools & Technology
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