Chapter 4 MAtrices and Determinants · 4.5 Solving Systems Using Inverse Matrices. Goals 1. Find and Use the inverse matrix to solve systems of linear equations. Vocabulary The n

Chapter 4 MAtrices and Determinants

4.4 Identity and Inverse Matrices4.5 Solving Systems Using Inverse Matrices

Goals1. Find and Use the inverse matrix to solve systems of

linear equations

VocabularyThe n X n identity matrix is the matrix that has 1’s on the main diagonal and 0’s elsewhere.

Two n X n matrices are inverses of each other if their product (in both orders) is the n X n identity matrix.

Find the Inverse Using a CalculatorSTEP 1: Select the second function button and then matrix.

STEP 2: Use the right arrow to move cursor to the EDIT column.

STEP 3: Select matrix #1

STEP 4: Enter the dimensions of the matrix.

STEP 5: Select second function, then QUIT to return to the calculation screen.

STEP 6: Select second function, then matrix, then #1 to place matrix A on your calculation screen.

STEP 7: Select the x-1 button. Your screen should read A-1.

STEP 8: Select ENTER. The answer matrix should appear on your screen.

Inverse

Inverse

Solving a Matrix EquationYou can use the inverse to solve a matrix equation of the form AX = B

STEP 1: Find A-1 (the inverse of A).

STEP 2: multiply both sides of the equation by A-1

STEP 3: The matrix you get by multiplying B by A-1 is X.

Solving a Matrix Equation

STEP 1: Find A-1 (the inverse of A).

Solving a Matrix Equation

STEP 1: Find A-1 (the inverse of A).

Solving a Matrix Equation

STEP 2: multiply both sides of the equation by A-1

Solving a Matrix Equation

STEP 2: multiply both sides of the equation by A-1

Solving a Matrix Equation

STEP 3: The matrix you get by multiplying B by A-1 is X.

Problems for 4.44.4 #13,19,25,29

4.5 solving systems using inverse matricesA linear system can be written as a matrix equation AX=B. The matrix A is the coefficient matrix of the system, X is the matrix of variables, and B is the matrix of constants.

Writing a Matrix equation

Solving a Linear System Using InverseSTEP 1: Write the linear system in matrix form.

STEP 2: Find the inverse of A.

STEP 3: Multiply B by A-1.

STEP 4: the variables are equal to the solution in STEP 3.

Solving a linear system

STEP 1: Write the linear system in matrix form.

Solving a linear system

STEP 1: Write the linear system in matrix form.

Solving a linear system

STEP 2: Find the inverse of A.

Solving a linear system

STEP 2: Find the inverse of A.

Solving a linear system

STEP 3: Multiply B by A-1.

Solving a linear system

STEP 3: Multiply B by A-1.

X = -7 and Y= -4

Problems 4.54.5 #11,23,35,37