Chapter 4 Section 5 and 6Finding and Using InversesAlgebra 2 NotesFebruary 26, 2009
Warm-UpsSolve each matrix equation for X:
Explain how to determine whether two matrices can be multiplied and what the dimensions of the product matrix will be.
Square MatrixLook on Page 199:
◦What is the definition of a square matrix??
(2 X 2) (3 X 3) etc…..
Review: Identity MatrixLook on Page 199:
◦What is the definition of a multiplicative identity matrix?
etc…
Inverse MatricesShow that B is the multiplicative
inverse of A:◦If B is an inverse of A then AB = I
DeterminantsA determinant will determine if a
matrix has an inverse◦ If the determinant = 0 then that matrix has
NO INVERSE!
det A = ad – bcFind the following determinants:
Solving Matrix Equations
Solve the following equation for X:
Matrix A
Matrix B
Solving a System of EquationsSystem of equations:
Matrix Equation:
Coefficient Matrix A
Variable Matrix X
Constant Matrix B
Solving a System of EquationsSolve the following system of
equations using inverse matrices:
Homework #31Page 203 #1*, 14-16**, 22, 25***• *Do #1 by hand!• **Use determinants to determine if it has a
inverse, then use the calculator to find the actual inverse for #14-16• ***Refer to Example 5 on pg 202 for #25
Page 217 #7, 8, 13, 14, 16, 23, 24, 30