4.5 Solving Systems of Equations Using Inverse Matrices
Warm Up:
3
&2
$4
5
$
$%' 1 3
' 1 # & x # &14 #
2 !! $$ y !! = $$34 !!
' 4!" $% z !" $%20!"
1.) Multiply the left side of the above equation.
2.) From #1, what system of equations does the above matrix equation
represent?
3.) Solve the above system of equations in three variables using the
linear combination method and determine where the three planes
intersect.
4.) Use Cramer’s Rule to solve the above system of equations.
5.) How can we use inverse matrices and our calculators to solve the
above system of equations ?
4.5 Solving Systems of Equations Using Inverse Matrices
PRACTICE:
1.) Use inverse matrices and your calculators to solve the following systems
of equations:
x + y + z = 10
5x – y = 1
3x + 4y + z = 8
Step 1: Set the system of equations up in matrix notation.
Step 2: Left multiply both sides of the matrix equation by the inverse of the
coefficient matrix.
2.) Use inverse matrices and your calculators to solve the following systems
of equations:
2x + y = -13
x – 3y = 11
Step 1: Set the system of equations up in matrix notation.
Step 2: Left multiply both sides of the matrix equation by the
inverse of the coefficient matrix.
Homework: p. 233-234 #31,32,36,37,39
4.5 Solving Systems of Equations Using Inverse Matrices