Warm UP: Review of Inequalities What do each of the symbols represent: 1. > 2. < Greater Than 2. Less than 3. Less than or equal to 4. Greater than or equal to Graph the inequalities

Section 10.5 – Applications of Matrices and Determinants After this section, you should be able to: Solve and graph inequalities Section 1.7 – Linear Inequalities AND Use matrices to find the area of a triangle Use matrices to determine if points are collinear

Find the area of the triangle whose vertices are: a) (5, 2), (7, 1), (-2, 3) The area of the triangle is b) (-2, 1), (0, 4), (3, 6) The area of the triangle is Use matrices to find the area of a triangle

(2, 7), (-3, -3), (5, 13) are collinear. Since determinant is zero, the three points are collinear Application 2 – Collinearity of Points Use a determinant to determine whether the points are collinear. Use matrices to determine if points are collinear

(1, -2), (-4, 1), (0, 3) The three points are NOT collinear Use a determinant to determine whether the points are collinear. Use matrices to determine if points are collinear

Section 10.5 – Applications of Matrices and Determinants After this section, you should be able to: Solve and graph inequalities Section 1.7 – Linear Inequalities AND Use matrices to find the area of a triangle Use matrices to determine if points are collinear HOMEWORK: Pg. 149 #44 (no calc) Solve and Graph & Pg. 763 # 13, 20, 29, 31

Section 10.5 day 2 – Cryptography A Cryptogram is a message written according to a secret code. Matrix multiplication can be used to encode and decode messages. First, each letter in the alphabet is assigned a number (with 0 assigned to a blank space). Then the message is converted to numbers and partitioned into uncoded row matrices, each having n entries. Example #1 – Given the alphabet assignment below, write the uncoded row matrix of order 1 x 3 for the message “MEET ME MONDAY”. 0 = _ 1 = A 2 = B 3 = C 4 = D 5 = E 6 = F 7 = G 8 = H 9 = I 10 = J 11 = K 12 = L 13 = M 14 = N 15 = O 16 = P 17 = Q 18 = R 19 = S 20 = T 21 = U 22 = V 23 = W 24 = X 25 = Y 26 = Z [ ] [ ] [ ] [ ] M E E T M E M O N D A Y [ ] *Note that a blank space is used to fill out the last uncoded row matrix

Section 10.5 day 2 – Cryptography To encode a message, choose an n x n invertible matrix such as A = *a square matrix that does not have a det = 0 This is what makes your encryption unique Multiply the uncoded row matrices by A (on the right) to obtain coded row matrices. [ ] = [ ] [ ] = [ ] = [ ] = [ ] = [ ] [ ] [ ] [ ] So, the sequence of coded row matrices is: [ ] Do this for each of the 1x 3 matrices and you will Have decoded the message MEET ME MONDAY