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ET 8.5

ET 8.5. COPY. Find the area of a triangle whose vertices are (1, 0), (2, 2), and (4, 3). = 1.5 SQ. UNITS. = - ½ (-3). Determine whether the points (-2, -2), (1, 1), and (7, 5) are collinear. Doesn’t equal zero NOT COLLINEAR. = - 6.

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ET 8.5

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  1. ET 8.5 COPY

  2. Find the area of a triangle whose vertices are (1, 0), (2, 2), and (4, 3). = 1.5 SQ. UNITS = - ½ (-3)

  3. Determine whether the points (-2, -2), (1, 1), and (7, 5) are collinear. Doesn’t equal zero NOT COLLINEAR = - 6

  4. A cryptogram is a message written according to a secretcode.

  5. Assign a number to each letter in the alphabet Write the uncoded row matrices of order 1 x 3 for the message MEET ME MONDAY n M E E T _ M E _ M O N D A Y [13 5 5] [20 0 13] [5 0 13] [15 14 4] [1 25 0]

  6. Write the uncoded row matrices of order 1 x 3 for the message MEET ME MONDAY n M E E T _ M E _ M O N D A Y [13 5 5] [20 0 13] [5 0 13] [15 14 4] [1 25 0] Now choose an n x n invertible matrix • Only a square matrix has a proper inverse. • A matrix has an inverse only if its’ determinant = 0. • Inverses can be found by Gaussian Elimination or memorized shortcut for 2x2.

  7. Write the uncoded row matrices of order 1 x 3 for the message n M E E T _ M E _ M O N D A Y [13 5 5] [20 0 13] [5 0 13] [15 14 4] [1 25 0] Multiply the uncoded row matrix by A (on the right) to obtain coded row matrices. = Uncoded Matrix Encoding Matrix A Coded Matrix = [13 -26 21] [13 5 5]

  8. M E E T _ M E _ M O N D A Y [13 5 5] [20 0 13] [5 0 13] [15 14 4] [1 25 0] = [13 -26 21] [13 5 5] A = [33 -53 -12] [20 0 13] A = [18 -23 -42] [5 0 13] A = [5 -20 56] [15 14 4] A = [-24 23 77] [1 25 0] A Coded row matrices [13 -26 21] [33 -53 -12] [18 -23 -42] [5 -20 56] [-24 23 77] Cryptogram 13 -26 21 33 -53 -12 18 -23 -42 5 -20 56 -24 23 77

  9. Now let’s decode the cryptogram Cryptogram 13 -26 21 33 -53 -12 18 -23 -42 5 -20 56 -24 23 77 Coded row matrices Now let’s decode the message. [13 -26 21] [33 -53 -12] [18 -23 -42] [5 -20 56] [-24 23 77] Find A-1. [13 -26 21] A-1 = [13 5 5] = [20 0 13] = [5 0 13] = [15 14 4] = [1 25 0] M E E [33 -53 -12] A-1 T _ M A-1 [18 -23 -42] E _ M [5 -20 56] O N D A-1 [-24 23 77] A-1 A Y _

  10. 8.5 Assignment • Day 1: 19, 27, 29, 30 31, 37 • Day 2: 46, 50, 52, 56

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