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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...

 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 matrix transformations to represent motion along a straight line.

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

 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 work with 2 × 2 matrices as transformations of the plane. Students combine matrices using matrix multiplication and addition. Students understand the role of the zero matrix...

 Student Outcomes Students understand that the absolute value of the determinant of a 2 × 2 matrix is the area of the image of the unit square.

 Student Outcomes Students understand that 2 × 2 matrix transformations are linear transformations taking straight lines to straight lines. Students understand that the absolute value of the...

 Student Outcomes Students determine inverse matrices using linear systems.

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

 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.

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

 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...

 Student Outcomes Students will review their understanding of linear transformations on real and complex numbers as well as linear transformations in twodimensional space. They will use their...

 Student Outcomes Students use parallelograms to interpret the sum of two points in ℝ geometrically. Students make a similar interpretation for the sum of two points in ℝ. Students recognize that...

 Student Outcomes Students verify that 3 x 3 matrices represent linear transformations from ℝ ⇒ℝ. Students investigate the matrices associated with transformations such as dilations and reflections...

 Student Outcomes Students construct matrices so that the linear transformation has a desired geometric effect. Students identify the geometric effect of the linear transformation based on the...

 Student Outcomes Students compose two linear transformations in the plane by multiplying the associated matrices. Students visualize composition of linear transformations in the plane.

 Student Outcomes Students use technology to perform compositions of linear transformations in ℝ.