Chapter 4 MAtrices and Determinants 4.4 Identity and Inverse Matrices 4.5 Solving Systems Using Inverse Matrices
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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
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