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 Precalculus Module 1: Complex Numbers and Transformations Module 1 sets the stage for expanding students' understanding of transformations by exploring the notion of linearity. This leads to the...

 Module 2 extends the concept of matrices introduced in Module 1. Students look at incidence relationships in networks and encode information about them via highdimensional matrices. Matrix...

 Topic C highlights the effectiveness of changing notations and the power provided by certain notations such as matrices. The study of vectors and matrices is introduced through a coherent connection...

 Topic B explores the geometric context for higherdimensional matrices. The geometric effect of matrix operations—matrix product, matrix sum, and scalar multiplication—are examined, and students...

 In Topic A, students look at incidence relationships in networks and encode information about them via highdimensional matrices. Questions on counting routes, the results of combining networks,...

 Student Outcomes Students use matrices to represent and manipulate data from network diagrams.

 Topic D opens with a formal definition of a vector. The arithmetical work for vector addition, subtraction, scalar multiplication, and vector magnitude is explored along with the geometrical...

 Student Outcomes Students add and subtract vectors and understand those operations geometrically and componentwise. Students understand scalar multiplication graphically and perform it component...

 Student Outcomes Students find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point. Students add vectors endtoend using the...

 Student Outcomes Students use matrices to represent data based on transportation networks. Students multiply a matrix by a scalar, add and subtract matrices of appropriate dimensions, and interpret...

 Student Outcomes Students understand the forces involved in constructing a stone arch. Students add and subtract vectors given in magnitude and direction form. Students solve problems that can be...

 Student Outcomes Students use matrix transformations to represent motion along a straight line.

 In Topic E students apply the knowledge developed in this module to understand how firstperson video games use matrix operations to project threedimensional objects onto twodimensional screens and...

 Student Outcomes Students use matrix transformations to model circular motion. Students use coordinate transformations to represent a combination of motions.

 Student Outcomes Students understand that an inverse transformation, when represented by a 2 × 2 matrix, exists precisely when the determinant of that matrix is nonzero.

 Student Outcomes Students write the equation for a line in ℝ2 or ℝ3 using vectors. Students write the parametric equations for a line in ℝ2 or ℝ3 . Students convert between parametric equations and...

 Student Outcomes Students apply linear transformations and vectors to understand the conditions required for a sequence of transformations to preserve the solution set to the system of equations.

 Student Outcomes Students represent linear transformations of the form L(x,y) = (ax + by, cx + dy) by matrix multiplication Students recognize when a linear transformation of the form ...

 Student Outcomes Students use vectors to define a translation map and translate geometric figures in ℝ and ℝ . Students represent and perform calculations with threedimensional vectors and...

 Student Outcomes Through discovery, students will understand how challenging it is to project threedimensional objects onto a twodimensional space. Students will understand that vanishing points...

 Student Outcomes Students work with 2 × 2 matrices as transformations of the plane. Students understand the role of the multiplicative identity matrix.

 Student Outcomes Students determine inverse matrices using linear systems.

 Student Outcomes Students use matrices to represent data based on transportation networks. Students multiply matrices of appropriate dimensions and interpret the meaning of this arithmetic in terms...

 Student Outcomes Students understand that an inverse transformation, when represented by a 2 × 2 matrix, exists precisely when the determinant of that matrix is nonzero.