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56 Results

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

 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 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 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 technology to perform compositions of linear transformations in ℝ.

 Student Outcomes Students discover and verify that matrix multiplication is distributive. Students discover and verify that matrix multiplication is associative.

 Student Outcomes Students prove both geometrically and algebraically that matrix addition is commutative.

 Student Outcomes Students study and practice the properties of matrix multiplication. Students understand the role of the multiplicative identity matrix.

 Student Outcomes Students represent complicated systems of equations, including 4×4 and 5×5 systems of equations, using matrix equations in the form Ax = b, where A represents the coefficient matrix...

 Student Outcomes Students understand that, unlike multiplication of numbers, matrix multiplication is not commutative.

 Student Outcomes Students will represent systems of three or more simultaneous equations as a linear transformation in the form Ax = b, where A represents the linear transformation, x represents the...

 Student Outcomes Students learn to project points in 3dimensional space onto a 2dimensional plane. Students learn how to simulate 3dimensional turning on a 2dimensional screen.

 Topic C provides a third context for the appearance of matrices via the study of systems of linear equations. Students see that a system of linear equations can be represented as a single matrix...

 Student Outcomes Students determine the complex roots of polynomial equations of the form xn = 1 and, more generally, equations of the form xn = k positive integers n and positive real numbers k....

 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 will create a short animation in ALICE 3.1 using onestep procedures. Students will apply their understanding of the mathematics of projecting threedimensional images onto...

 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 apply their understanding of polynomial identities that have been extended to the complex numbers to find the square roots of complex numbers.

 Student Outcomes Students understand how a formula for the nth roots of a complex number is related to powers of a complex number. Students calculate the nth roots of a complex number.

 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 solve problems involving physical phenomena that can be represented by vectors.

 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 will represent systems of equations as linear transformations of the form Lx = b, using matrix notation. Students will discover that the systems of equations written in the...