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All of Unit 5 
Unit 51: 
Basic Matrix Operations (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.VM.7: Multiply matrices by scalars to produce new matrices.
MGSE912.N.VM.8: Add, subtract, and multiply matrices of appropriate dimensions.
MGSE912.N.VM.10:Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
MGSE912.N.VM.9:Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
Video Lessons: (p1, p2, p3, p4a, p4b, p4c)
Visualizing Multiplication of Matrices:
Chart Method, Train Method
Sample Quiz: (Interactive, PDF)


Unit 52: 
Matrix Inverses & Determinants(Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.VM.10:Understand that, unlike multiplication of numbers, matrix multiplication for square matrices is not a commutative operation, but still satisfies the associative and distributive properties.
MGSE912.N.VM.9:Understand that the zero and identity matrices play a role in matrix addition and multiplication similar to the role of 0 and 1 in the real numbers. The determinant of a square matrix is nonzero if and only if the matrix has a multiplicative inverse.
MGSE912.N.VM.12:Work with 2 X 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area.
MGSE912.N.VM.12:Represent a system of linear equations as a single matrix equation in a vector variable.
MGSE912.A.REI.9:Find the inverse of a matrix if it exists and use it to solve systems of linear equations (using technology for matrices of dimension 3 × 3 or greater).
GSP Animation Area of the Parallelogram
Video Lessons: (p1, p2, p3, p4)
Sample Quiz: (Interactive, PDF)


Unit 53: 
Informational Matrices (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.VM.6:Use matrices to represent and manipulate data, e.g., transformations of vectors.
MGSE912.N.VM.7: Multiply matrices by scalars to produce new matrices.
MGSE912.N.VM.8:Add, subtract, and multiply matrices of appropriate dimensions.
Video Lessons: (p1, p2)
Sample Quiz:(Interactive, PDF) 

Unit 54: 
Transformational Matrices (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.VM.6:Use matrices to represent and manipulate data, e.g., transformations of vectors.
MGSE912.N.VM.7: Multiply matrices by scalars to produce new matrices.
MGSE912.N.VM.8:Add, subtract, and multiply matrices of appropriate dimensions.
MGSE912.N.VM.12:Work with 2 X 2 matrices as transformations of the plane and interpret the absolute value of the determinant in terms of area.
GSP Animation Transformations
Proof of General Rotation Matrix (PDF)
Video Lessons: (p1, p2, p3, p4, p5, p6)
Sample Quiz:(Interactive, PDF)


Unit 55: 
Basic Vector Forms (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.VM.1: Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes (e.g., v, v, v, v).
MGSE912.N.VM.2 Find the components of a vector by subtracting the coordinates of an initial point from the coordinates of a terminal point.
MGSE912.N.VM.3: Solve problems involving velocity and other quantities that can be represented by vectors.
Video Lessons: (p1, p2, p3, p4, p5)
Sample Quiz:(Interactive, PDF)


Unit 56: 
Basic Vector Operations (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.VM.4 :Add and subtract vectors.
MGSE912.N.VM4a: Add vectors endtoend, componentwise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes.
MGSE912.N.VM4b: Given two vectors in magnitude and direction form, determine the magnitude and direction of their sum.
MGSE912.N.VM4c: Understand vector subtraction v – w as v + (–w), where (–w) is the additive inverse of w, with the same magnitude as w and pointing in the opposite direction. Represent vector subtraction graphically by connecting the tips in the appropriate order, and perform vector subtraction componentwise.
MGSE912.N.VM.5 :Multiply a vector by a scalar
MGSE912.N.VM.5a: Represent scalar multiplication graphically by scaling vectors and possibly reversing their direction; perform scalar multiplication componentwise, e.g., as c(vx, vy) = (cvx, cvy).
MGSE912.N.VM.5b: Compute the magnitude of a scalar multiple cv using cv = cv. Compute the direction of cv knowing that when cv = 0, the direction of cv is either along v (for c > 0) or against v (for c < 0).
Video Lessons: (p1, p2, p3, p4a, p4b, p5a, p5b)
Sample Quiz:(Interactive, PDF)


Unit 57: 
Vector Matrix Transforms (Doc, PDF, Key)
Georgia Standards of Excellence (Click to Expand)
MGSE912.N.VM.11 :Multiply a vector (regarded as a matrix with one column) by a matrix of suitable dimensions to produce another vector. Work with matrices as transformations of vectors.
Video Lessons: (p1, p2)
Sample Quiz:(Interactive, PDF)


TEST: 
Testing Item Banks for Exam View
(305 available questions for Unit 5)
Password Required
ExamView Video Instructions (How To Make a Test)
Author: Matt Winking 

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