1. INTRODUCTION TO MATRICES 4.1 AND 4.2 DAY 1

2. DO NOW Grab some slides from the front and solve this: Example: The local shop sells 3 types of pies. Beef pies cost $3 each Chicken pies cost $4 each Vegetable pies cost $2 each And this is how many they sold in 4 days: Calculate the sales for each day.

3. WHERE WE ARE AND WHERE WE ARE GOING TODAY (10/12): 4.1 and 4.2 (Introduction to Matrices) THURSDAY (10/13): 4.2 (Applying Matrix Multiplication) FRIDAY (10/14) and MONDAY (10/17): 4.3 (Determinants and Cramer’s Rule) MONDAY (10/17): Princess Project Due! TUESDAY (10/18): 4.1-4.3 Performance Assessment

4. That’s RC Cola!

5. Would you like to solve THis….BY hand

6. ESSENTIAL VOCABULARY Matrix : a rectangular array of numeric or algebraic quantities subject to mathematical operations For example, A is a matrix. The dimensions of A are 3x4 (RC Cola!). The numbers are called entries.

7. THE MATRIX ZOO! Row matrix A matrix with only 1 row Column matrix A matrix with only 1 column Square matrix A matrix with the same number of rows and columns

8. MORE ANIMALS! Zero matrix A matrix with all entries equal to 0 Identity matrix (of size n) An nxn matrix with ones on the main diagonal and zeroes elsewhere

9. ADDING AND SUBTRACTING MATRIX ELEMENTS Only if they have the same dimensions! Example: How about - ???

10. MULTIPLY A MATRIX BY A SCALAR For the following matrix A, find 2 A and –1 A.

11. MATRIX EQUATIONS 4*(-2x)=-48, so x=6 and 4(2y+6)=6, so 8y+24=6, so y=-9/4 2y+5=-5, so y=-5 and -6+x=-7, so x=-1

12. MATRIX MULTIPLICATION: SIZE MATTERS! If A is an m x n matrix, and B is an n x p matrix, then the product AB is an m x p matrix The number of columns of A must equal the number of rows of B for matrix multiplication to be defined. http://www.mathresource.iitb.ac.in/linear%20algebr a/example2.0.1/index.html http://www.mathresource.iitb.ac.in/linear%20algebr a/example2.0.1/index.html Example: =

13. MULTIPLY IF POSSIBLE =

14. Refer back to “Do Now” Now think about this... the value of sales for Monday is calculated this way: Beef pie value + Chicken pie value + Vegetable pie value $3×13 + $4×8 + $2×6 = $83 So it is, in fact, the "dot product" of prices and how many were sold: ($3, $4, $2) (13, 8, 6) = $3×13 + $4×8 + $2×6 = $83 We match the price to how many sold, multiply them, then sum the result.

17. GRAPHING CALCULATOR (TI-83): MULTIPLYING MATRICES Let’s verify this one: Hit “MATRX” (TI-84, 2 nd X^(-1)) Scroll to Edit Press 1 Enter dimensions of first matrix (3X2), Press Enter Put in your entries, hit Enter after each entry Hit “MATRX”, “Edit” again. This time, select [B] (2X3) Now hit “2 nd -MODE” to get to main screen and hit “MATRX”, “1”, “X (times)”, “MATRX”, “2”, “ENTER

18. Hmmmm….. Using your calculator and the same two matrices, now compute B*A. What do you notice? Try entering the 3X3 identity matrix for A and multiplying it by any matrix B with the same dimensions. What do you notice?

19. APPLET http://www.mathresource.iitb.ac.in/linear%20algebr a/example2.0.1/index.html http://www.mathresource.iitb.ac.in/linear%20algebr a/example2.0.1/index.html