2. CHAPTER 4 LESSON 3 Multiplying Matrices

3. VOCABULARY  NONE

4. MULTIPLYING MATRICES  You can multiply two matrices if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix.  A mxn x B pxq n and p must be equal  The resulting matrix would be AB mxq

5. EXAMPLES  A 2x6 x B 6x4 = AB 2x4  A 1x3 x B 3x4 =  A 2x3 x B 3x2 =

6. PROPERTIES OF MATRICES  Associative Property of Matrix Multiplication (AB)C=A(BC)  Associative Property of Scalar Multiplication c(AB)=(cA)B=A(cB)  Left Distributive Property C(A+B)=CA+CB  Right Distributive Property (A+B)C=AC+BC If equations are not written exactly like they are here, they are not true

7. MULTIPLYING MATRICES ab cd X fg hi = af+bhag+bi cf+dhcg+di

8. EXAMPLES 10-2 -73 X 14 5-2 = 5 8 X 34 =

9. MULTIPLYING MATRICES  IF ONLY THERE WAS AN EASIER WAY……..

10. THE EASIER WAY  On your calculator  Press 2 nd, then press the x -1 button  Go right two tabs to EDIT  Select [A]  Enter dimensions of first matrix  Fill in matrix  Go back to Edit menu, Select [B]  Enter dimensions of second matrix  Fill in matrix

11. CONTINUED  Press 2 nd button, then press MODE button to exit out of matrix menu  Press 2 nd button, then press x -1 button  Select [A]  Press multiplication button  Press 2 nd button, then press x -1 button  Select [B]  Press Enter  Answer is given in matrix form

12. EXAMPLES 1234 5678 9098 7654 3210 x 98765 43210 12345 67890 =

13. HOMEWORK  Worksheet 4-3