Содержание
- 2. Barnett/Ziegler/Byleen Finite Mathematics 11e Identity Matrix for Multiplication 1 is called the multiplicative identity for real
- 3. Barnett/Ziegler/Byleen Finite Mathematics 11e Identity Matrices 2 x 2 identity matrix: 3 x 3 identity matrix
- 4. Barnett/Ziegler/Byleen Finite Mathematics 11e Identity Matrix Multiplication AI = A (Verify the multiplication) We can also
- 5. Barnett/Ziegler/Byleen Finite Mathematics 11e Inverse of a Matrix All real numbers (excluding 0) have an inverse.
- 6. Barnett/Ziegler/Byleen Finite Mathematics 11e Matrix Inverses Some (not all) square matrices also have matrix inverses If
- 7. Barnett/Ziegler/Byleen Finite Mathematics 11e Inverse of a 2x2 Matrix There is a simple procedure to find
- 8. Barnett/Ziegler/Byleen Finite Mathematics 11e Inverse of a 2x2 matrix (continued) Step 1: Determine whether or not
- 9. Barnett/Ziegler/Byleen Finite Mathematics 11e Inverse of a 2x2 matrix (continued) Step 2. Reverse the entries on
- 10. Barnett/Ziegler/Byleen Finite Mathematics 11e Inverse of a 2x2 matrix (continued) The inverse of the matrix is
- 11. Barnett/Ziegler/Byleen Finite Mathematics 11e Inverse of a General Square Matrix 1. Augment the matrix with the
- 12. Barnett/Ziegler/Byleen Finite Mathematics 11e Example: Inverse of a 3x3 Matrix Find the inverse of Step 1.
- 13. Barnett/Ziegler/Byleen Finite Mathematics 11e Example (continued) Step 3. Multiply row 2 by (1/3) to get a
- 14. Barnett/Ziegler/Byleen Finite Mathematics 11e Example (continued) Step 7. Eliminate the (5/3) in the first row, third
- 15. Barnett/Ziegler/Byleen Finite Mathematics 11e Example Solution The inverse matrix appears on the right hand side of
- 16. Barnett/Ziegler/Byleen Finite Mathematics 11e Application: Cryptography Matrix inverses can provide a simple and effective procedure for
- 17. Barnett/Ziegler/Byleen Finite Mathematics 11e Any matrix A whose elements are positive integers and whose inverse exists
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