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H.1. Matrices and Systems of Equations

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H.1.Q. Unit Challenge
H.1.1. Writing Matrices and Solving Systems
1. H.1.1.O. Overview
2. H.1.1.1. Determine the order of the matrix
3. H.1.1.2. Write the augmented matrix for the system of linear equations
4. H.1.1.3. Determine whether each matrix is in row-echelon form
5. H.1.1.4. Write the matrix in row-echelon form
6. H.1.1.5. Solve the system using matrices

H.2. Operations with Matrices

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H.2.Q. Unit Challenge
H.2.1. Matrix Addition and Scalar Multiplication
1. H.2.1.O. Overview
2. H.2.1.1. Solve for the variables in the matrix equation
3. H.2.1.2. Add or subtract the matrices
4. H.2.1.3. Use scalar multiplication on the matrix
5. H.2.1.4. Solve a matrix equation

H.2.2. Matrix Multiplication
1. H.2.2.O. Overview
2. H.2.2.1. Find the product of two matrices
3. H.2.2.2. Solve a system of linear equations using matrix multiplication

H.3. The Inverse and Determinant of a Square Matrix

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H.3.Q. Unit Challenge
H.3.1. Finding and Using the Inverse of a Matrix
1. H.3.1.O. Overview
2. H.3.1.1. Tell whether the two matrices are inverses
3. H.3.1.2. Find the inverse of the matrix by adjoining the identity matrix
4. H.3.1.3. Find the inverse of a 2 x 2 matrix using the inverse formula
5. H.3.1.4. Solve the system using an inverse matrix

H.3.2. Finding and Using the Determinant of a Matrix
1. H.3.2.O. Overview
2. H.3.2.1. Find the determinant of a 2 x 2 matrix
3. H.3.2.2. Solve the equation for x using the determinant
4. H.3.2.3. Find the minor of the matrix
5. H.3.2.4. Find the cofactor of the matrix
6. H.3.2.5. Find the determinant of a 3 x 3 matrix
7. H.3.2.6. Find the determinant of a 4 x 4 matrix

H.4. Applications of Matrices and Determinants

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H.4.Q. Unit Challenge
H.4.1. Cramer’s Rule
1. H.4.1.O. Overview
2. H.4.1.1. Use Cramer’s Rule to solve a 2 x 2 system
3. H.4.1.2. Use Cramer’s Rule to solve a 3 x 3 system

H.4.2. Area of a Triangle
1. H.4.2.O. Overview
2. H.4.2.1. Find the Area of a Triangle given the three vertices
3. H.4.2.2. Find the value of the variable so that the triangle with the given vertices has the given area

H.4.3. Collinear Points
1. H.4.3.O. Overview
2. H.4.3.1. Use the determinant to determine whether the given points are collinear
3. H.4.3.2. Find the value of the variable such that all the points are collinear
4. H.4.3.3. Use a determinant to find the equation of the line passing through the two points

H.4.4. Encoding and Decoding Messages
1. H.4.4.O. Overview
2. H.4.4.1. Write the uncoded row matrices for a message and use an invertible matrix to encode a message
3. H.4.4.2. Use the inverse matrix to decode a cryptogram