MATRICES Jeffrey Bivin Lake Zurich High School Last Updated: October 12, 2005

Inverses and Identities 5x = 3 Jeff Bivin -- LZHS

Now with Matrices This is the Identity Matrix for 2 x 2 Matrices Jeff Bivin -- LZHS

Let’s look at another example Jeff Bivin -- LZHS

New Question What do we multiply a matrix by to get the Identity? Jeff Bivin -- LZHS

The Inverse of a 2x2 Matrix Jeff Bivin -- LZHS

The Inverse of a 2x2 Matrix Jeff Bivin -- LZHS

The Inverse of a 2x2 Matrix Jeff Bivin -- LZHS

This is our Formula! Jeff Bivin -- LZHS

This is our Formula! Jeff Bivin -- LZHS

This is our Formula! Jeff Bivin -- LZHS

Are the two Matrices Inverses? Jeff Bivin -- LZHS The product of inverse matrices is the identity matrix. Identity, therefore, INVERSE Matrices

Are the two Matrices Inverses? Jeff Bivin -- LZHS The product of inverse matrices is the identity matrix. Not the Identity, therefore, NOT INVERSE Matrices

Jeff Bivin -- LZHS Does the Matrix have an Inverse? Let’s review the definition of the Inverse of a 2x2 Matrix

The Inverse of a 2x2 Matrix Jeff Bivin -- LZHS

Find the determinant! Jeff Bivin -- LZHS Therefore, NO inverse! Does the Matrix have an Inverse?

Find the determinant! Jeff Bivin -- LZHS Therefore, an inverse exists! Does the Matrix have an Inverse?

Find the determinant! Jeff Bivin -- LZHS Therefore, NO inverse! Does the Matrix have an Inverse?

Find the determinant! Jeff Bivin -- LZHS Does the Matrix have an Inverse? Therefore, an inverse exists!

This is our Formula! Jeff Bivin -- LZHS 3x + 2y = 7 4x - 5y = 11 Solve the system using inverse matrices

This is our Formula! Jeff Bivin -- LZHS 2x - 4y = 9 3x - 2y = 1 Solve the system using inverse matrices