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4.1 and 4.2 Day 1

4.1 and 4.2 Day 1. Introduction to matrices. 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 :

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4.1 and 4.2 Day 1

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  1. 4.1 and 4.2 Day 1 Introduction to matrices

  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 2A and –1A.

  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 pmatrix • 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%20algebra/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.

  15. Graphing Calculator (TI-83): Multiplying Matrices • Let’s verify this one: • Hit “MATRX” (TI-84, 2nd 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 “2nd-MODE” to get to main screen and hit “MATRX”, “1”, “X (times)”, “MATRX”, “2”, “ENTER

  16. 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?

  17. Applet • http://www.mathresource.iitb.ac.in/linear%20algebra/example2.0.1/index.html

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