INTRODUCTION TO MATRICES 4.1 AND 4.2 DAY 1. DO NOW Grab some slides from the front and solve this: Example: The local shop sells 3 types of pies. Beef.

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Presentation transcript:

INTRODUCTION TO MATRICES 4.1 AND 4.2 DAY 1

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.

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): Performance Assessment

That’s RC Cola!

Would you like to solve THis….BY hand

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.

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

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

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

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

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

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. a/example2.0.1/index.html a/example2.0.1/index.html Example: =

MULTIPLY IF POSSIBLE =

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.

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

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?

APPLET a/example2.0.1/index.html a/example2.0.1/index.html