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4.5, 4.6 2 x 2 and 3 x 3 Matrices, Determinants, and Inverses

4.5, 4.6 2 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

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4.5, 4.6 2 x 2 and 3 x 3 Matrices, Determinants, and Inverses

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  1. 4.5, 4.62 x 2 and 3 x 3 Matrices, Determinants, and Inverses Date: _____________

  2. 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

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

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

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

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

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

  8. Find the determinant of each 3x3 Matrix.

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

  10. 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

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

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

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

  14. Linear Equations Matrix Equations Solve for X.

  15. Objective - To solve systems using inverse matrices.

  16. Do this one on your own to see if you understand

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