Algebra and Trigonometry: Graphs and Models (6th Edition)
Algebra and Trigonometry: Graphs and Models (6th Edition)
6th Edition
ISBN: 9780134179049
Author: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna
Publisher: PEARSON
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Chapter 9.1, Problem 59E
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Question 4 (a) The following matrices represent linear maps on R² with respect to an orthonormal basis: = [1/√5 2/√5 [2/√5 -1/√5] " [1/√5 2/√5] A = B = [2/√5 1/√5] 1 C = D = = = [ 1/3/5 2/35] 1/√5 2/√5 -2/√5 1/√5' For each of the matrices A, B, C, D, state whether it represents a self-adjoint linear map, an orthogonal linear map, both, or neither. (b) For the quadratic form q(x, y, z) = y² + 2xy +2yz over R, write down a linear change of variables to u, v, w such that q in these terms is in canonical form for Sylvester's Law of Inertia. [6] [4]
part b please
Question 5 (a) Let a, b, c, d, e, ƒ Є K where K is a field. Suppose that the determinant of the matrix a cl |df equals 3 and the determinant of determinant of the matrix a+3b cl d+3e f ГЪ e [ c ] equals 2. Compute the [5] (b) Calculate the adjugate Adj (A) of the 2 × 2 matrix [1 2 A = over R. (c) Working over the field F3 with 3 elements, use row and column operations to put the matrix [6] 0123] A = 3210 into canonical form for equivalence and write down the canonical form. What is the rank of A as a matrix over F3? 4

Chapter 9 Solutions

Algebra and Trigonometry: Graphs and Models (6th Edition)

Ch. 9.1 - Prob. 11ECh. 9.1 - Prob. 12ECh. 9.1 - Prob. 13ECh. 9.1 - Prob. 14ECh. 9.1 - Prob. 15ECh. 9.1 - Prob. 16ECh. 9.1 - Prob. 17ECh. 9.1 - Prob. 18ECh. 9.1 - Prob. 19ECh. 9.1 - Prob. 20ECh. 9.1 - Prob. 21ECh. 9.1 - Prob. 22ECh. 9.1 - Prob. 23ECh. 9.1 - Prob. 24ECh. 9.1 - Prob. 25ECh. 9.1 - Prob. 26ECh. 9.1 - Prob. 27ECh. 9.1 - Prob. 28ECh. 9.1 - Prob. 29ECh. 9.1 - Prob. 30ECh. 9.1 - Prob. 31ECh. 9.1 - Prob. 32ECh. 9.1 - Prob. 33ECh. 9.1 - Prob. 34ECh. 9.1 - Prob. 35ECh. 9.1 - Prob. 36ECh. 9.1 - Prob. 37ECh. 9.1 - Prob. 38ECh. 9.1 - Prob. 39ECh. 9.1 - Prob. 40ECh. 9.1 - Prob. 41ECh. 9.1 - Prob. 42ECh. 9.1 - Prob. 43ECh. 9.1 - Prob. 44ECh. 9.1 - Prob. 45ECh. 9.1 - Prob. 46ECh. 9.1 - Prob. 47ECh. 9.1 - Prob. 48ECh. 9.1 - Prob. 49ECh. 9.1 - Prob. 50ECh. 9.1 - Prob. 51ECh. 9.1 - Prob. 52ECh. 9.1 - Prob. 53ECh. 9.1 - Prob. 54ECh. 9.1 - Prob. 55ECh. 9.1 - Prob. 56ECh. 9.1 - Prob. 57ECh. 9.1 - Concert Ticket Prices. One evening 1500 concert...Ch. 9.1 - Prob. 59ECh. 9.1 - Prob. 60ECh. 9.1 - Prob. 61ECh. 9.1 - Prob. 62ECh. 9.1 - Nutrition. A one-cup serving of spaghetti with...Ch. 9.1 - Prob. 64ECh. 9.1 - Prob. 65ECh. 9.1 - Prob. 66ECh. 9.1 - Prob. 67ECh. 9.1 - Prob. 68ECh. 9.1 - Prob. 69ECh. 9.1 - Prob. 70ECh. 9.1 - Prob. 71ECh. 9.1 - Prob. 72ECh. 9.1 - Prob. 73ECh. 9.1 - Prob. 74ECh. 9.1 - Prob. 75ECh. 9.1 - Prob. 76ECh. 9.1 - Prob. 77ECh. 9.1 - Prob. 78ECh. 9.1 - Prob. 79ECh. 9.1 - Prob. 80ECh. 9.1 - Prob. 81ECh. 9.1 - Prob. 82ECh. 9.1 - Prob. 83ECh. 9.1 - Prob. 84ECh. 9.1 - Prob. 85ECh. 9.1 - Antifreeze Mixtures. An automobile radiator...Ch. 9.1 - Prob. 87ECh. 9.1 - Prob. 88ECh. 9.1 - Prob. 89ECh. 9.2 - Prob. 1ECh. 9.2 - Prob. 2ECh. 9.2 - Prob. 3ECh. 9.2 - Prob. 4ECh. 9.2 - Prob. 5ECh. 9.2 - Prob. 6ECh. 9.2 - Prob. 7ECh. 9.2 - Prob. 8ECh. 9.2 - Prob. 9ECh. 9.2 - Prob. 10ECh. 9.2 - Prob. 11ECh. 9.2 - Prob. 12ECh. 9.2 - Prob. 13ECh. 9.2 - Prob. 14ECh. 9.2 - Prob. 15ECh. 9.2 - Prob. 16ECh. 9.2 - Paralympic Medals. At the 2014 Paralympic Games in...Ch. 9.2 - Restaurant Meals. The total number of...Ch. 9.2 - Prob. 19ECh. 9.2 - Prob. 20ECh. 9.2 - Prob. 21ECh. 9.2 - Jolts of Caffeine. One 8-oz serving each of brewed...Ch. 9.2 - Pet Ownership. In a recent year, Americans owned a...Ch. 9.2 - Mail-Order Business. Natural Fibers Clothing...Ch. 9.2 - Foreign Aid. In 2013, the top three donors of...Ch. 9.2 - Spring Cleaning. In a group of 100 adults, 70 say...Ch. 9.2 - Nutrition. A hospital dietician must plan a lunch...Ch. 9.2 - Prob. 28ECh. 9.2 - Prob. 29ECh. 9.2 - Prob. 30ECh. 9.2 - Prob. 31ECh. 9.2 - Prob. 32ECh. 9.2 - Prob. 33ECh. 9.2 - Prob. 34ECh. 9.2 - Prob. 35ECh. 9.2 - Prob. 36ECh. 9.2 - Prob. 37ECh. 9.2 - Prob. 38ECh. 9.2 - Prob. 39ECh. 9.2 - Prob. 40ECh. 9.2 - Prob. 41ECh. 9.2 - Prob. 42ECh. 9.2 - Prob. 43ECh. 9.2 - Prob. 44ECh. 9.2 - Prob. 45ECh. 9.2 - Prob. 46ECh. 9.2 - Prob. 47ECh. 9.2 - Prob. 48ECh. 9.2 - Prob. 49ECh. 9.2 - Prob. 50ECh. 9.2 - Prob. 51ECh. 9.2 - Prob. 52ECh. 9.3 - Prob. 1ECh. 9.3 - Prob. 2ECh. 9.3 - Prob. 3ECh. 9.3 - Prob. 4ECh. 9.3 - Prob. 5ECh. 9.3 - Prob. 6ECh. 9.3 - Prob. 7ECh. 9.3 - Prob. 8ECh. 9.3 - Prob. 9ECh. 9.3 - Prob. 10ECh. 9.3 - Prob. 11ECh. 9.3 - Prob. 12ECh. 9.3 - Prob. 13ECh. 9.3 - Prob. 14ECh. 9.3 - Prob. 15ECh. 9.3 - Prob. 16ECh. 9.3 - Prob. 17ECh. 9.3 - Prob. 18ECh. 9.3 - Prob. 19ECh. 9.3 - Prob. 20ECh. 9.3 - Prob. 21ECh. 9.3 - Prob. 22ECh. 9.3 - Prob. 23ECh. 9.3 - Prob. 24ECh. 9.3 - Solve the system of equations using Gaussian...Ch. 9.3 - Prob. 26ECh. 9.3 - Prob. 27ECh. 9.3 - Prob. 28ECh. 9.3 - Prob. 29ECh. 9.3 - Prob. 30ECh. 9.3 - Prob. 31ECh. 9.3 - Prob. 32ECh. 9.3 - Prob. 33ECh. 9.3 - Prob. 34ECh. 9.3 - Prob. 35ECh. 9.3 - Prob. 36ECh. 9.3 - Prob. 37ECh. 9.3 - Prob. 38ECh. 9.3 - Prob. 39ECh. 9.3 - Prob. 40ECh. 9.3 - Prob. 41ECh. 9.3 - Prob. 42ECh. 9.3 - Prob. 43ECh. 9.3 - Prob. 44ECh. 9.3 - Prob. 45ECh. 9.3 - Prob. 46ECh. 9.3 - Prob. 47ECh. 9.3 - Prob. 48ECh. 9.3 - Prob. 49ECh. 9.3 - Prob. 50ECh. 9.3 - Prob. 51ECh. 9.3 - Prob. 52ECh. 9.3 - Prob. 53ECh. 9.3 - Prob. 54ECh. 9.3 - Prob. 55ECh. 9.3 - Prob. 56ECh. 9.3 - Prob. 57ECh. 9.3 - Prob. 58ECh. 9.3 - Prob. 59ECh. 9.3 - Prob. 60ECh. 9.3 - Prob. 61ECh. 9.3 - Prob. 62ECh. 9.4 - Prob. 1ECh. 9.4 - Prob. 2ECh. 9.4 - Prob. 3ECh. 9.4 - Prob. 4ECh. 9.4 - Prob. 5ECh. 9.4 - Prob. 6ECh. 9.4 - Prob. 7ECh. 9.4 - Prob. 8ECh. 9.4 - Prob. 9ECh. 9.4 - Prob. 10ECh. 9.4 - Prob. 11ECh. 9.4 - Prob. 12ECh. 9.4 - Prob. 13ECh. 9.4 - Prob. 14ECh. 9.4 - Prob. 15ECh. 9.4 - Prob. 16ECh. 9.4 - Prob. 17ECh. 9.4 - Prob. 18ECh. 9.4 - Prob. 19ECh. 9.4 - Prob. 20ECh. 9.4 - Prob. 21ECh. 9.4 - Prob. 22ECh. 9.4 - Prob. 23ECh. 9.4 - Prob. 24ECh. 9.4 - Prob. 25ECh. 9.4 - Prob. 26ECh. 9.4 - Prob. 27ECh. 9.4 - Prob. 28ECh. 9.4 - Produce. The produce manager at Stan’s Market...Ch. 9.4 - Prob. 30ECh. 9.4 - Prob. 31ECh. 9.4 - Prob. 32ECh. 9.4 - Prob. 33ECh. 9.4 - Prob. 34ECh. 9.4 - Prob. 35ECh. 9.4 - Prob. 36ECh. 9.4 - Prob. 37ECh. 9.4 - Prob. 38ECh. 9.4 - Prob. 39ECh. 9.4 - Prob. 40ECh. 9.4 - Prob. 41ECh. 9.4 - Prob. 42ECh. 9.4 - Prob. 43ECh. 9.4 - Prob. 44ECh. 9.4 - Prob. 45ECh. 9.4 - Prob. 46ECh. 9.4 - Prob. 47ECh. 9.4 - Prob. 48ECh. 9.4 - Prob. 49ECh. 9.4 - Prob. 50ECh. 9.4 - Prob. 51ECh. 9.4 - Prob. 52ECh. 9.4 - Prob. 53ECh. 9.4 - Prob. 54ECh. 9.5 - Prob. 1ECh. 9.5 - Prob. 2ECh. 9.5 - Prob. 3ECh. 9.5 - Prob. 4ECh. 9.5 - Prob. 5ECh. 9.5 - Prob. 6ECh. 9.5 - Prob. 7ECh. 9.5 - Prob. 8ECh. 9.5 - Prob. 9ECh. 9.5 - Prob. 10ECh. 9.5 - Prob. 11ECh. 9.5 - Prob. 12ECh. 9.5 - Prob. 13ECh. 9.5 - Prob. 14ECh. 9.5 - Prob. 15ECh. 9.5 - Prob. 16ECh. 9.5 - Prob. 17ECh. 9.5 - Prob. 18ECh. 9.5 - Prob. 19ECh. 9.5 - Prob. 20ECh. 9.5 - Prob. 21ECh. 9.5 - Prob. 22ECh. 9.5 - Prob. 23ECh. 9.5 - Prob. 24ECh. 9.5 - Prob. 25ECh. 9.5 - Prob. 26ECh. 9.5 - Prob. 27ECh. 9.5 - Prob. 28ECh. 9.5 - Prob. 29ECh. 9.5 - Prob. 30ECh. 9.5 - Prob. 31ECh. 9.5 - Prob. 32ECh. 9.5 - Prob. 33ECh. 9.5 - Solve the system of equations using the inverse of...Ch. 9.5 - Prob. 35ECh. 9.5 - Prob. 36ECh. 9.5 - Prob. 37ECh. 9.5 - Prob. 38ECh. 9.5 - Prob. 39ECh. 9.5 - Prob. 40ECh. 9.5 - Prob. 41ECh. 9.5 - Prob. 42ECh. 9.5 - Prob. 43ECh. 9.5 - Prob. 44ECh. 9.5 - Prob. 45ECh. 9.5 - Prob. 46ECh. 9.5 - Prob. 47ECh. 9.5 - Prob. 48ECh. 9.5 - Prob. 49ECh. 9.5 - Prob. 50ECh. 9.5 - Prob. 51ECh. 9.5 - Prob. 52ECh. 9.5 - Prob. 53ECh. 9.5 - Prob. 54ECh. 9.6 - Prob. 1ECh. 9.6 - Prob. 2ECh. 9.6 - Prob. 3ECh. 9.6 - Prob. 4ECh. 9.6 - Prob. 5ECh. 9.6 - Prob. 6ECh. 9.6 - Prob. 7ECh. 9.6 - Prob. 8ECh. 9.6 - Prob. 9ECh. 9.6 - Prob. 10ECh. 9.6 - Prob. 11ECh. 9.6 - Prob. 12ECh. 9.6 - Prob. 13ECh. 9.6 - Prob. 14ECh. 9.6 - Prob. 15ECh. 9.6 - Prob. 16ECh. 9.6 - Prob. 17ECh. 9.6 - Prob. 18ECh. 9.6 - Prob. 19ECh. 9.6 - Prob. 20ECh. 9.6 - Prob. 21ECh. 9.6 - Prob. 22ECh. 9.6 - Prob. 23ECh. 9.6 - Prob. 24ECh. 9.6 - Prob. 25ECh. 9.6 - Prob. 26ECh. 9.6 - Prob. 27ECh. 9.6 - Prob. 28ECh. 9.6 - Prob. 29ECh. 9.6 - Prob. 30ECh. 9.6 - Prob. 31ECh. 9.6 - Prob. 32ECh. 9.6 - Prob. 33ECh. 9.6 - Prob. 34ECh. 9.6 - Prob. 35ECh. 9.6 - Prob. 36ECh. 9.6 - Prob. 37ECh. 9.6 - Prob. 38ECh. 9.6 - Prob. 39ECh. 9.6 - Prob. 40ECh. 9.6 - Prob. 41ECh. 9.6 - Prob. 42ECh. 9.6 - Prob. 43ECh. 9.6 - Prob. 44ECh. 9.6 - Prob. 45ECh. 9.6 - Prob. 46ECh. 9.6 - Prob. 47ECh. 9.6 - Prob. 48ECh. 9.6 - Prob. 49ECh. 9.6 - Prob. 50ECh. 9.6 - Prob. 51ECh. 9.6 - Prob. 52ECh. 9.6 - Prob. 53ECh. 9.6 - Prob. 54ECh. 9.6 - Prob. 55ECh. 9.6 - Prob. 56ECh. 9.6 - Prob. 57ECh. 9.6 - Prob. 58ECh. 9.6 - Prob. 59ECh. 9.6 - Prob. 60ECh. 9.7 - Prob. 1ECh. 9.7 - Prob. 2ECh. 9.7 - Prob. 3ECh. 9.7 - Prob. 4ECh. 9.7 - Prob. 5ECh. 9.7 - Prob. 6ECh. 9.7 - Prob. 7ECh. 9.7 - Prob. 8ECh. 9.7 - Prob. 9ECh. 9.7 - Prob. 10ECh. 9.7 - Prob. 11ECh. 9.7 - Prob. 12ECh. 9.7 - Prob. 13ECh. 9.7 - Prob. 14ECh. 9.7 - Prob. 15ECh. 9.7 - Prob. 16ECh. 9.7 - Prob. 17ECh. 9.7 - Prob. 18ECh. 9.7 - Prob. 19ECh. 9.7 - Prob. 20ECh. 9.7 - Prob. 21ECh. 9.7 - Prob. 22ECh. 9.7 - Prob. 23ECh. 9.7 - Prob. 24ECh. 9.7 - Prob. 25ECh. 9.7 - Prob. 26ECh. 9.7 - Prob. 27ECh. 9.7 - Prob. 28ECh. 9.7 - Prob. 29ECh. 9.7 - Prob. 30ECh. 9.7 - Prob. 31ECh. 9.7 - Prob. 32ECh. 9.7 - Prob. 33ECh. 9.7 - Prob. 34ECh. 9.7 - Prob. 35ECh. 9.7 - Prob. 36ECh. 9.7 - Prob. 37ECh. 9.7 - Prob. 38ECh. 9.7 - Prob. 39ECh. 9.7 - Prob. 40ECh. 9.7 - Prob. 41ECh. 9.7 - Prob. 42ECh. 9.7 - Prob. 43ECh. 9.7 - Prob. 44ECh. 9.7 - Prob. 45ECh. 9.7 - Prob. 46ECh. 9.7 - Prob. 47ECh. 9.7 - Prob. 48ECh. 9.7 - Prob. 49ECh. 9.7 - Prob. 50ECh. 9.7 - Prob. 51ECh. 9.7 - Prob. 52ECh. 9.7 - Prob. 53ECh. 9.7 - Prob. 54ECh. 9.7 - Prob. 55ECh. 9.7 - Prob. 56ECh. 9.7 - Prob. 57ECh. 9.7 - Prob. 58ECh. 9.7 - Prob. 59ECh. 9.7 - Prob. 60ECh. 9.7 - Prob. 61ECh. 9.7 - Prob. 62ECh. 9.7 - Prob. 63ECh. 9.7 - Prob. 64ECh. 9.7 - Prob. 65ECh. 9.7 - Maximizing Income. Golden Harvest Foods makes...Ch. 9.7 - Prob. 67ECh. 9.7 - Prob. 68ECh. 9.7 - Prob. 69ECh. 9.7 - Prob. 70ECh. 9.7 - Prob. 71ECh. 9.7 - Prob. 72ECh. 9.7 - Prob. 73ECh. 9.7 - Prob. 74ECh. 9.7 - Prob. 75ECh. 9.7 - Prob. 76ECh. 9.7 - Prob. 77ECh. 9.7 - Prob. 78ECh. 9.7 - Prob. 79ECh. 9.7 - Prob. 80ECh. 9.7 - Prob. 81ECh. 9.7 - Prob. 82ECh. 9.7 - Prob. 83ECh. 9.7 - Prob. 84ECh. 9.7 - Prob. 85ECh. 9.7 - Prob. 86ECh. 9.7 - Prob. 87ECh. 9.7 - Prob. 88ECh. 9.7 - Prob. 89ECh. 9.7 - Prob. 90ECh. 9.7 - Prob. 91ECh. 9.8 - Prob. 1ECh. 9.8 - Prob. 2ECh. 9.8 - Prob. 3ECh. 9.8 - Prob. 4ECh. 9.8 - Prob. 5ECh. 9.8 - Prob. 6ECh. 9.8 - Decompose into partial fractions. Check your...Ch. 9.8 - Prob. 8ECh. 9.8 - Prob. 9ECh. 9.8 - Prob. 10ECh. 9.8 - Prob. 11ECh. 9.8 - Decompose into partial fractions. Check your...Ch. 9.8 - Prob. 13ECh. 9.8 - Prob. 14ECh. 9.8 - Prob. 15ECh. 9.8 - Prob. 16ECh. 9.8 - Prob. 17ECh. 9.8 - Prob. 18ECh. 9.8 - Prob. 19ECh. 9.8 - Prob. 20ECh. 9.8 - Prob. 21ECh. 9.8 - Prob. 22ECh. 9.8 - Prob. 23ECh. 9.8 - Prob. 24ECh. 9.8 - Prob. 25ECh. 9.8 - Prob. 26ECh. 9.8 - Prob. 27ECh. 9.8 - Prob. 28ECh. 9.8 - Prob. 29ECh. 9.8 - Prob. 30ECh. 9.8 - Prob. 31ECh. 9.8 - Prob. 32ECh. 9.8 - Prob. 33ECh. 9.8 - Prob. 34ECh. 9.8 - Prob. 35ECh. 9 - Prob. 1MCCh. 9 - Prob. 2MCCh. 9 - Prob. 3MCCh. 9 - Prob. 4MCCh. 9 - Prob. 5MCCh. 9 - Prob. 6MCCh. 9 - Prob. 7MCCh. 9 - Prob. 8MCCh. 9 - Prob. 9MCCh. 9 - Prob. 10MCCh. 9 - Prob. 11MCCh. 9 - Prob. 12MCCh. 9 - Prob. 13MCCh. 9 - Prob. 14MCCh. 9 - Prob. 15MCCh. 9 - Prob. 16MCCh. 9 - Prob. 17MCCh. 9 - Prob. 18MCCh. 9 - Prob. 19MCCh. 9 - Prob. 20MCCh. 9 - Prob. 21MCCh. 9 - Prob. 1RECh. 9 - Prob. 2RECh. 9 - Prob. 3RECh. 9 - Prob. 4RECh. 9 - Prob. 5RECh. 9 - Prob. 6RECh. 9 - Prob. 7RECh. 9 - Prob. 8RECh. 9 - Prob. 9RECh. 9 - Prob. 10RECh. 9 - Prob. 11RECh. 9 - Prob. 12RECh. 9 - Prob. 13RECh. 9 - Prob. 14RECh. 9 - Prob. 15RECh. 9 - Prob. 16RECh. 9 - Prob. 17RECh. 9 - Prob. 18RECh. 9 - Prob. 19RECh. 9 - Prob. 20RECh. 9 - Prob. 21RECh. 9 - Prob. 22RECh. 9 - Prob. 23RECh. 9 - Prob. 24RECh. 9 - Prob. 25RECh. 9 - Prob. 26RECh. 9 - Prob. 27RECh. 9 - Prob. 28RECh. 9 - Prob. 29RECh. 9 - Prob. 30RECh. 9 - Prob. 31RECh. 9 - Prob. 32RECh. 9 - Prob. 33RECh. 9 - Prob. 34RECh. 9 - Prob. 35RECh. 9 - Prob. 36RECh. 9 - Prob. 37RECh. 9 - Prob. 38RECh. 9 - Prob. 39RECh. 9 - Find A–1, if it exists. Ch. 9 - Prob. 41RECh. 9 - Prob. 42RECh. 9 - Prob. 43RECh. 9 - Prob. 44RECh. 9 - Prob. 45RECh. 9 - Prob. 46RECh. 9 - Prob. 47RECh. 9 - Prob. 48RECh. 9 - Prob. 49RECh. 9 - Prob. 50RECh. 9 - Solve using Cramer’s rule. [6.6] Ch. 9 - Prob. 52RECh. 9 - Prob. 53RECh. 9 - Prob. 54RECh. 9 - Prob. 55RECh. 9 - Prob. 56RECh. 9 - Prob. 57RECh. 9 - Prob. 58RECh. 9 - Prob. 59RECh. 9 - Prob. 60RECh. 9 - Prob. 61RECh. 9 - Prob. 62RECh. 9 - Prob. 63RECh. 9 - Prob. 64RECh. 9 - Prob. 65RECh. 9 - Prob. 66RECh. 9 - Prob. 67RECh. 9 - Prob. 68RECh. 9 - Prob. 69RECh. 9 - Prob. 1TCh. 9 - Prob. 2TCh. 9 - Prob. 3TCh. 9 - Prob. 4TCh. 9 - Prob. 5TCh. 9 - Prob. 6TCh. 9 - Prob. 7TCh. 9 - Prob. 8TCh. 9 - Prob. 9TCh. 9 - Prob. 10TCh. 9 - Prob. 11TCh. 9 - Prob. 12TCh. 9 - Prob. 13TCh. 9 - Prob. 14TCh. 9 - Prob. 15TCh. 9 - Prob. 16TCh. 9 - Prob. 17TCh. 9 - Prob. 18TCh. 9 - Prob. 19TCh. 9 - Prob. 20TCh. 9 - Prob. 21TCh. 9 - Prob. 22TCh. 9 - Prob. 23TCh. 9 - Prob. 24TCh. 9 - Prob. 25T
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