GSM Algebra I GSM Geometry GSM Algebra II GSM PreCalc Other Courses Calculus I GSM - Adv. Math Decision Making Analytical Geometry ```CP-Statistics ``` `All Units` Coordinate Algebra Integrated Algebra I Integrated Geometry GPS Middle School Math Home > GSM Algebra 2 >Unit 6 - Linear Algebra & Matrices

Search Site:

Review

 Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8

Georgia:
All of Unit 6
Unit 6-1: Systems of Linear Equations (Doc, PDF, Key)
Georgia Standards (Click to Expand)
MGSE9-12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, simple rational, and exponential functions (integer inputs only).

MGSE9-12.A.CED.3 Represent constraints by equations or inequalities, and by systems of equation and/or inequalities, and interpret data points as possible (i.e. a solution) or not possible (i.e. a non-solution) under the established constraints.

Video Lessons: (p1, p2, p3, p4, p5a, p5b)

Sample Quiz:(Interactive, PDF)

Unit 6-2: Systems of Linear Inequalities (Doc, PDF, Key)
Georgia Standards (Click to Expand)
MGSE9-12.A.CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, simple rational, and exponential functions (integer inputs only).

Video Lessons: (p1, p2, p3, p4a, p4b)

Sample Quiz:(Interactive, PDF)

Unit 6-3: Solving Equations by Graphing (Doc, PDF, Key)
Georgia Standards (Click to Expand)

MGSE9-12.A.REI.11 Using graphs, tables, or successive approximations, show that the solution to the equation f(x) = g(x) is the x-value where the y-values of f(x) and g(x) are the same.

Video Lessons: (p1, p2)

Sample Quiz:(Interactive, PDF)

Unit 6-4: Basic Matrix Operations (Doc, PDF, Key)
Georgia Standards (Click to Expand)
MGSE9-12.N.VM.7: Multiply matrices by scalars to produce new matrices.

MGSE9-12.N.VM.8: Add, subtract, and multiply matrices of appropriate dimensions.

MGSE9-12.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.

MGSE9-12.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 6-5: Matrix Inverses & Determinants (Doc, PDF, Key)
Georgia Standards (Click to Expand)
MGSE9-12.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.

MGSE9-12.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.

MGSE9-12.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.

MGSE9-12.N.VM.12:Represent a system of linear equations as a single matrix equation in a vector variable.

MGSE9-12.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).

Area of the Parallelogram

Video Lessons: (p1, p2, p3, p4)

Sample Quiz:(Interactive, PDF)

Unit 6-6: Informational Matrices (Doc, PDF, Key)
Georgia Standards (Click to Expand)
MGSE9-12.N.VM.6:Use matrices to represent and manipulate data, e.g., transformations of vectors.

MGSE9-12.N.VM.7:
Multiply matrices by scalars to produce new matrices.

MGSE9-12.N.VM.8:
Add, subtract, and multiply matrices of appropriate dimensions

Video Lessons: (p1, p2)

Sample Quiz:(Interactive, PDF)

Unit 6-7: Transformational Matrices (Doc, PDF, Key)
Georgia Standards (Click to Expand)
MGSE9-12.N.VM.6:Use matrices to represent and manipulate data, e.g., transformations of vectors.

MGSE9-12.N.VM.7:
Multiply matrices by scalars to produce new matrices.

MGSE9-12.N.VM.8:
Add, subtract, and multiply matrices of appropriate dimensions.

MGSE9-12.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.

Proof of General Rotation Matrix (PDF)

Video Lessons: (p1, p2, p3, p4, p5, p6)

Sample Quiz:(Interactive, PDF)

TEST: Testing Item Banks for Exam View

(371 available questions for Unit 6)