8.3 The Inverse of a Square MatrixObjective: Find and use the inverse matrix to solve systems of linear equations.

Standard: Linear Algebra 9.0

What's a MULTIPLICATIVE INVERSE??

To be an inverse matrix:

Ex. 1) Show that B is the Inverse of A.

Do all matrices have an inverse?

Singular:

Nonsingular (aka: ________)

Ex. 2) Find the inverse of A if it exists.

A=

The "Shortcut" for a 2x2 matrixIf… and…

ad – bc ≠ 0

then…

Ex. 2 Revisited) Find the inverse of A if it exists.

Ex. 3) Find the inverse of A if it exists.

A=

Inverse of a 3x3 Matrix

Using Inverses for Systems of Equations

The coefficient matrix…

Ex. 4) Solve the systems using matrices.

Ex. 5) Solve the system using matrices.

Assignment:

#12 p. 608 #4, 6, 11, 15, 17, 20, 25, 27, 53, 60, 63

Quiz #3 (8.2 and 8.3) on Tuesday/Wednesday Feb. 22-23