Gifted Precalculus

1
Gifted Precalculus

• Section 8.3
• The Inverse of a Square Matrix

2
What is the multiplicativeinverse of 3?

• What is 3 x 1/3 ?
• What is 1/3 x 3?
• What is 1 called?

3
The Identity Matrix

• The n x n matrix that consists of 1s on its main
  diagonal and 0s elsewhere is called the identity
  matrix of order n and is denoted by

4
The Inverse of a Square Matrix

• Let A be an n x n matrix. If there exists a
  matrix A-1 such that
• AA-1 A-1A In
• then A-1 is called the inverse of A,
• read A inverse.

5
The Inverse of a 2 x 2 Matrix
6
Find the inverse of the matrix if it exists.
7
Solve the equation.

• 3x 7

8
Use an inverse matrix to solve the system of
linear equations.
9
Use the matrix capabilities of the calculator to
solve the system.