4.5, x 2 and 3 x 3 Matrices, Determinants, and Inverses Date: _____________

Matrices are multiplicative inverses Page 199 – 2 definitions Multiplicative Identity Matrix – Must be a square matrix, 2 x 2, 3 x 3, 4 x 4, etc. – Has 1’s in the main diagonal and 0’s elsewhere Multiplicative Inverse of a Matrix – when multiplying a matrix by its inverse, we get the identity matrix

Use your calculator Matrices are multiplicative inverses Show that these two matrices are multiplicative inverses

Objective - To evaluate the determinates of 2 x 2 and 3 x 3 matrices. Determinant can be labeled either way Find the Determinant

Determinant Objective - To evaluate the determinates of 2 x 2 and 3 x 3 matrices. Find the Determinant

Evaluate the Determinant for each Matrix When the determinant = 0, then that matrix has NO INVERSE

Determinant Take the first 2 columns and rewrite them outside Find the determinant of each 3x3 Matrix.

Fun? Use your Calculator Matrix, over to MATH, then det(, then go to Matrix, we want matrix A

Determinant and its use The determinant is used to find our inverse We will use our calculator to find the inverse. Type in: Find the determinant first: Therefore, it has an inverse

Determinant and its use The determinant is used to find our inverse We will use our calculator to find the inverse. Type in:

Find the inverse of the matrix If A didn’t have an inverse, you’d get the message ERR: SINGULAR MAT

Checking your answers. If you multiply inverses, you will always get the identity matrix. This is a way you can check your answers

Solve for X. Linear EquationsMatrix Equations

Objective - To solve systems using inverse matrices.

Do this one on your own to see if you understand