Matrices
Notes
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Resources
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Standards
Perform operations on matrices and use matrices in applications
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.9 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.10 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.
Solve systems of equations
MGSE9-12.A.REI.8 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)
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.9 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.10 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.
Solve systems of equations
MGSE9-12.A.REI.8 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)