HSN-VM.C.10

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- HSN-VM.C.6(+) Use matrices to represent and manipulate data, e.g., to represent payoffs or incidence relationships in a network.
- HSN-VM.C.7(+) Multiply matrices by scalars to produce new matrices, e.g., as when all of the payoffs in a game are doubled.
- HSN-VM.C.8(+) Add, subtract, and multiply matrices of appropriate dimensions.
- HSN-VM.C.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.
- HSN-VM.C.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.
- HSN-VM.C.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.
- HSN-VM.C.12(+) Work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

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## HSN-VM.C.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.

7 Lesson(s)

### Manufacturing Cat Toys (Day 2 of 2)

12th Grade Math »
Unit: Matrices and Systems

12th Grade Math »
Unit: Matrices and Systems

Big Idea:

#### We can set up matrix equations - now it is time to solve them!

Standards:

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(1)

Resources
(6)

Big Idea:

#### Students answer questions on their personal response systems to guide the review for the test.

Standards:

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(6)

Big Idea:

#### Students discover how to find the inverse of a matrix by analyzing the relationships between matrices and their inverses.

Standards:

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(3)

Resources
(15)

Big Idea:

#### After discovering how to find the determinant students will use it to find inverses of 2X2 matrices.

Standards:

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(1)

Resources
(16)

### Do Matrices Work Like Real Numbers?

12th Grade Math »
Unit: Matrices

12th Grade Math »
Unit: Matrices

Big Idea:

#### Through exploration students discover that some properties of real numbers will not exist for matrices.

Standards:

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(1)

Resources
(14)

Big Idea:

#### Students will demonstrate their learning of Matrices in this formal assessment.

Standards:

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(3)

Big Idea:

#### Through a scratch off game students review important concepts of matrices

Standards:

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(1)

Resources
(11)

Common Core Math

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### Middle School

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

HS Number & Quantity

HS Algebra

HS Functions

HS Geometry

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

Eighth Grade

Ninth and Tenth Grade

Kindergarten

First grade

Second grade

Third Grade

Fourth grade

Fifth grade

Middle School