Lesson 1: Basic Matrix Operations
Lesson 2: Multiplying Matrices
Lesson 3: Matrix Determinants and Cramer's Rule
Lesson 4: Inverse Matrices
Finding Inverse Matrices
The n x n identity matrix is a matrix with ones for all elements on the main diagonal (top left to bottom right) and zeros for all the other elements
If A is any n x n matrix and I is the n x n identity matrix, then AI = A and IA = A
Two n x n matrices A and B are inverses of each other when their product is the n x n identity matrix; AB = I and BA = I
An n x n matrix A has an inverse if and only if det A ≠0
The inverse of A is denoted by A-1
The Inverse of a 2x2 Matrix
Using an Inverse Matrix to Solve a Linear System
Write the system as a matrix equation AX = B; the matrix A is the coefficient matrix, X is the matrix of variables, and B is the matrix of constants
Find the inverse of matrix A
Multiply each side of AX = B by A-1 on the left to find the solution X = A-1B
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