Use Inverse Matrices to Solve Linear Systems

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Presentation transcript:

Use Inverse Matrices to Solve Linear Systems Section 3.8: Use Inverse Matrices to Solve Linear Systems

Identity matrix – a matrix with 1’s on the main diagonal and 0’s elsewhere. 2 x 2 Identity Matrix Identity Matrix

Inverses – Two n x n matrices A and B are inverses of each other if their product (in both orders) is the n x n identity matrix.

Inverse of a 2 x 2 matrix The inverse of the matrix is provided that ad – bc ≠ 0.

Using an Inverse Matrix to Solve a Linear System Step 1: 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. Step 2: Find the inverse of matrix A. Step 3: Multiply each side of AX = B by A-1 on the left to find the solution X = A-1B.

Example 1: Find the inverse of

Example 2: Find the inverse of each matrix. a) b) c)

HOMEWORK (Day 1) Pg. 215; 3 – 10

Example 3: Solve the matrix equation AX = B for the 2 x 2 matrix X.

Example 4: Use an inverse matrix to solve the linear system Example 4: Use an inverse matrix to solve the linear system. -2x + 3y = -11 5x + y = 19

HOMEWORK (Day 2) Pg. 214 – 215; 13 – 15, 25 – 27