1. Section 4.5 Identity and Inverse Matrices

2. 1 0 0 0 1 0 0 0 1 1 0 0 0 1 0 0 0 1 Def: A constant matrix with 1’s on the diagonal and 0’s everywhere else is called the identity matrix Multiply -2 4 7 5 -3 6 -8 2 -1 = (-2 + 0 + 0) (0 + 4 + 0)(0 + 0 -7) (5 + 0 + 0)(0 -3 + 0)(0 + 0 + 6) (-8 + 0 + 0)(0 + 2 + 0)(0 + 0 -1) = -2 4 7 5 -3 6 -8 2 -1 You get the same matrix

3. If the Identity matrix is designated as I then for any square matrix “A”: AI = AalsoIA = A commutative The notation for inverse matrix is: Notation: (Inverse of matrix M) A -1 For matrices, the -1 is not an exponent

4. Def: When you multiply a matrix by its inverse matrix the product is the Identity Matrix AA -1 = I =

5. Def: Any matrix will have an inverse If and only if and Note: not all matrices have inverses

6. 1.) Use your calculator to find the inverse matrix for: http://www.youtube.com/ watch?v=_fFj4NbLcTU

7. 2.) Use your calculator to find the inverse matrix for:

8. 3.) Determine whether the following is true or false:

9. Using your calculator Enter the matrix into your calculator 2ndMatrix Edit At this point just follow the prompts Quit2nd Return to the home screen 2ndMatrix Arrow down to the matrix you defined in Step 1 above Enter Step Call out the matrix to your home screen Description 1 Key-strokes 2 3

10. Using your calculator Find the inverse of your matrix x -1 The inverse should now appear on your home screen StepDescription 4 Key-strokes Use math, enter, enter to change decimals To fractions

11. Homework Page 217 Problems: 11- 19, 21-29(odd)