Mat 150 – Class #24
Objectives
Find the inverse of a matrix Find matrix inverses with technology Solve matrix equations Solve matrix equations with technology
Inverse MatricesTwo square matrices, A and B, are called inverses of each other if
AB = I and BA = Iwhere I is the identity matrix. We denote this by B = A–1 and A = B–1.
Example
Solve that A and B are inverses matrices if
Solution
1 0.6 0.2 2 2 1
0 0.4 0.2 and 1 3 1
1 0.4 0.8 2 1 2
A B
Examples
a) Find the inverse of Solution
b) If , solve for .
2 1 2
1 0 1
4 2 3
A
Example
Solve the system
by writing a matrix equation and using an inverse matrix.Solution
2 2 5
2
4 2 3 4
x y z
x z
x y z
Example
Ace Trucking Company has an order for delivery of three products: A, B, and C. If the company can carry 30,000 cubic feet and 62,000 pounds and is insured for $276,000, how many units of each product can be carried?
Assignment
Pg.544-548 #1-23 odd #25 #30
Quiz Monday November 24 which will be over lectures from Class 21 thru Class 23
Some Key Concepts:
• Solve systems of linear equations in three variables using left-to-right elimination
• Find solutions of dependent systems
• Determine when a system of equations is inconsistent
• Represent systems of equations with matrices
• Identify an identity matrix
• Form an augmented matrix
• Identify a coefficient matrix
• Reduce a matrix with row operations
• Reduce a matrix to its row-echelon form
• Add two matrices
• Subtract two matrices
• Multiply a matrix by a constant
• Multiply two matrices
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