Essentials of College Algebra (11th Edition)
11th Edition
ISBN: 9780321912251
Author: Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher: PEARSON
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Question
Chapter R.4, Problem 19E
To determine
To factor:
The polynomial
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You are given a plane Π in R3 defined by two vectors, p1 and p2, and a subspace W in R3 spanned by twovectors, w1 and w2. Your task is to project the plane Π onto the subspace W.First, answer the question of what the projection matrix is that projects onto the subspace W and how toapply it to find the desired projection. Second, approach the task in a different way by using the Gram-Schmidtmethod to find an orthonormal basis for subspace W, before then using the resulting basis vectors for theprojection. Last, compare the results obtained from both methods
Plane II is spanned by the vectors:
- (2) · P² - (4)
P1=2
P21
3
Subspace W is spanned by the vectors:
2
W1
- (9) ·
1
W2
1
= (³)
Chapter R Solutions
Essentials of College Algebra (11th Edition)
Ch. R.1 - Prob. 1ECh. R.1 - Prob. 2ECh. R.1 - Prob. 3ECh. R.1 - Prob. 4ECh. R.1 - Prob. 5ECh. R.1 - Prob. 6ECh. R.1 - Prob. 7ECh. R.1 - Prob. 8ECh. R.1 - Prob. 9ECh. R.1 - Prob. 10E
Ch. R.1 - Prob. 11ECh. R.1 - Prob. 12ECh. R.1 - Prob. 13ECh. R.1 - Prob. 14ECh. R.1 - Prob. 15ECh. R.1 - Prob. 16ECh. R.1 - Prob. 17ECh. R.1 - Prob. 18ECh. R.1 - Prob. 19ECh. R.1 - Prob. 20ECh. R.1 - Prob. 21ECh. R.1 - Prob. 22ECh. R.1 - Prob. 23ECh. R.1 - Prob. 24ECh. R.1 - Prob. 25ECh. R.1 - Prob. 26ECh. R.1 - Prob. 27ECh. R.1 - Prob. 28ECh. R.1 - Prob. 29ECh. R.1 - Prob. 30ECh. R.1 - Prob. 31ECh. R.1 - Prob. 32ECh. R.1 - Prob. 33ECh. R.1 - Prob. 34ECh. R.1 - Prob. 35ECh. R.1 - Prob. 36ECh. R.1 - Prob. 37ECh. R.1 - Prob. 38ECh. R.1 - Prob. 39ECh. R.1 - Prob. 40ECh. R.1 - Prob. 41ECh. R.1 - Prob. 42ECh. R.1 - Prob. 43ECh. R.1 - Prob. 44ECh. R.1 - Prob. 45ECh. R.1 - Prob. 46ECh. R.1 - Prob. 47ECh. R.1 - Prob. 48ECh. R.1 - Prob. 49ECh. R.1 - Prob. 50ECh. R.1 - Prob. 51ECh. R.1 - Prob. 52ECh. R.1 - Prob. 53ECh. R.1 - Prob. 54ECh. R.1 - Prob. 55ECh. R.1 - Prob. 56ECh. R.1 - Prob. 57ECh. R.1 - Prob. 58ECh. R.1 - Prob. 59ECh. R.1 - Prob. 60ECh. R.1 - Prob. 61ECh. R.1 - Prob. 62ECh. R.1 - Prob. 63ECh. R.1 - Prob. 64ECh. R.1 - Prob. 65ECh. R.1 - Prob. 66ECh. R.1 - Prob. 67ECh. R.1 - Prob. 68ECh. R.1 - Prob. 69ECh. R.1 - Prob. 70ECh. R.1 - Prob. 71ECh. R.1 - Prob. 72ECh. R.1 - Prob. 73ECh. R.1 - Prob. 74ECh. R.1 - Prob. 75ECh. R.1 - Prob. 76ECh. R.1 - Prob. 77ECh. R.1 - Prob. 78ECh. R.1 - Prob. 79ECh. R.1 - Prob. 80ECh. R.1 - Prob. 81ECh. R.1 - Prob. 82ECh. R.1 - Prob. 83ECh. R.1 - Prob. 84ECh. R.1 - Prob. 85ECh. R.1 - Prob. 86ECh. R.1 - Prob. 87ECh. R.1 - Prob. 88ECh. R.1 - Prob. 89ECh. R.1 - Prob. 90ECh. R.1 - Prob. 91ECh. R.1 - Prob. 92ECh. R.1 - Prob. 93ECh. R.1 - Prob. 94ECh. R.2 - Prob. 1ECh. R.2 - Prob. 2ECh. R.2 - Prob. 3ECh. R.2 - Prob. 4ECh. R.2 - Prob. 5ECh. R.2 - Prob. 6ECh. R.2 - Prob. 7ECh. R.2 - Prob. 8ECh. R.2 - Prob. 9ECh. R.2 - Prob. 10ECh. R.2 - Prob. 11ECh. R.2 - Prob. 12ECh. R.2 - Prob. 13ECh. R.2 - Prob. 14ECh. R.2 - Prob. 15ECh. R.2 - Prob. 16ECh. R.2 - Prob. 17ECh. R.2 - Prob. 18ECh. R.2 - Prob. 19ECh. R.2 - Prob. 20ECh. R.2 - Prob. 21ECh. R.2 - Prob. 22ECh. R.2 - Prob. 23ECh. R.2 - Prob. 24ECh. R.2 - Prob. 25ECh. R.2 - Prob. 26ECh. R.2 - Prob. 27ECh. R.2 - Prob. 28ECh. R.2 - Prob. 29ECh. R.2 - Prob. 30ECh. R.2 - Prob. 31ECh. R.2 - Prob. 32ECh. R.2 - Prob. 33ECh. R.2 - Prob. 34ECh. R.2 - Prob. 35ECh. R.2 - Prob. 36ECh. R.2 - Prob. 37ECh. R.2 - Prob. 38ECh. R.2 - Prob. 39ECh. R.2 - Prob. 40ECh. R.2 - Prob. 41ECh. R.2 - Prob. 42ECh. R.2 - Prob. 43ECh. R.2 - Prob. 44ECh. R.2 - Prob. 45ECh. R.2 - Prob. 46ECh. R.2 - Prob. 47ECh. R.2 - Prob. 48ECh. R.2 - Prob. 49ECh. R.2 - Prob. 50ECh. R.2 - Prob. 51ECh. R.2 - Prob. 52ECh. R.2 - Prob. 53ECh. R.2 - Prob. 54ECh. R.2 - Prob. 55ECh. R.2 - Prob. 56ECh. R.2 - Prob. 57ECh. R.2 - Prob. 58ECh. R.2 - Prob. 59ECh. R.2 - Prob. 60ECh. R.2 - Prob. 61ECh. R.2 - Prob. 62ECh. R.2 - Prob. 63ECh. R.2 - Prob. 64ECh. R.2 - Prob. 65ECh. R.2 - Prob. 66ECh. R.2 - Prob. 67ECh. R.2 - Prob. 68ECh. R.2 - Prob. 69ECh. R.2 - Prob. 70ECh. R.2 - Prob. 71ECh. R.2 - Prob. 72ECh. R.2 - Prob. 73ECh. R.2 - Prob. 74ECh. R.2 - Prob. 75ECh. R.2 - Prob. 76ECh. R.2 - Prob. 77ECh. R.2 - Prob. 78ECh. R.2 - Prob. 79ECh. R.2 - Prob. 80ECh. R.2 - Prob. 81ECh. R.2 - Prob. 82ECh. R.2 - Prob. 83ECh. R.2 - Prob. 84ECh. R.2 - Prob. 85ECh. R.2 - Prob. 86ECh. R.2 - Prob. 87ECh. R.2 - Prob. 88ECh. R.2 - Prob. 89ECh. R.2 - Prob. 90ECh. R.2 - Prob. 91ECh. R.2 - Prob. 92ECh. R.2 - Prob. 93ECh. R.2 - Prob. 94ECh. R.2 - Prob. 95ECh. R.2 - Prob. 96ECh. R.2 - Prob. 97ECh. R.2 - Prob. 98ECh. R.2 - Prob. 99ECh. R.2 - Prob. 100ECh. R.2 - Prob. 101ECh. R.2 - Prob. 102ECh. R.2 - Prob. 103ECh. R.2 - Prob. 104ECh. R.2 - Prob. 105ECh. R.2 - Prob. 106ECh. R.2 - Prob. 107ECh. R.2 - Prob. 108ECh. R.2 - Prob. 109ECh. R.2 - Prob. 110ECh. R.2 - Prob. 111ECh. R.2 - Prob. 112ECh. R.2 - Prob. 113ECh. R.2 - Prob. 114ECh. R.2 - Prob. 115ECh. R.2 - Prob. 116ECh. R.2 - Prob. 117ECh. R.2 - Prob. 118ECh. R.2 - Prob. 119ECh. R.2 - Prob. 120ECh. R.2 - Prob. 121ECh. R.2 - Prob. 122ECh. R.2 - Prob. 123ECh. R.2 - Prob. 124ECh. R.2 - Prob. 125ECh. R.2 - Prob. 126ECh. R.2 - Prob. 127ECh. R.2 - Prob. 128ECh. R.2 - Prob. 129ECh. R.2 - Prob. 130ECh. R.2 - Prob. 131ECh. R.2 - Prob. 132ECh. R.2 - Prob. 133ECh. R.2 - Prob. 134ECh. R.3 - Prob. 1ECh. R.3 - Prob. 2ECh. R.3 - Prob. 3ECh. R.3 - Prob. 4ECh. R.3 - Prob. 5ECh. R.3 - Prob. 6ECh. R.3 - Prob. 7ECh. R.3 - Prob. 8ECh. R.3 - Prob. 9ECh. R.3 - Prob. 10ECh. R.3 - Prob. 11ECh. R.3 - Prob. 12ECh. R.3 - Prob. 13ECh. R.3 - Prob. 14ECh. R.3 - Prob. 15ECh. R.3 - Prob. 16ECh. R.3 - Prob. 17ECh. R.3 - Prob. 18ECh. R.3 - Prob. 19ECh. R.3 - Prob. 20ECh. R.3 - Prob. 21ECh. R.3 - Prob. 22ECh. R.3 - Prob. 23ECh. R.3 - Prob. 24ECh. R.3 - Prob. 25ECh. R.3 - Prob. 26ECh. R.3 - Prob. 27ECh. R.3 - Prob. 28ECh. R.3 - Prob. 29ECh. R.3 - Prob. 30ECh. R.3 - Prob. 31ECh. R.3 - Prob. 32ECh. R.3 - Prob. 33ECh. R.3 - Prob. 34ECh. R.3 - Prob. 35ECh. R.3 - Prob. 36ECh. R.3 - Prob. 37ECh. R.3 - Prob. 38ECh. R.3 - Prob. 39ECh. R.3 - Prob. 40ECh. R.3 - Prob. 41ECh. R.3 - Prob. 42ECh. R.3 - Prob. 43ECh. R.3 - Prob. 44ECh. R.3 - Prob. 45ECh. R.3 - Prob. 46ECh. R.3 - Prob. 47ECh. R.3 - Prob. 48ECh. R.3 - Prob. 49ECh. R.3 - Prob. 50ECh. R.3 - Prob. 51ECh. R.3 - Prob. 52ECh. R.3 - Prob. 53ECh. R.3 - Prob. 54ECh. R.3 - Prob. 55ECh. R.3 - Prob. 56ECh. R.3 - Prob. 57ECh. R.3 - Prob. 58ECh. R.3 - Prob. 59ECh. R.3 - Prob. 60ECh. R.3 - Prob. 61ECh. R.3 - Prob. 62ECh. R.3 - Prob. 63ECh. R.3 - Prob. 64ECh. R.3 - Prob. 65ECh. R.3 - Prob. 66ECh. R.3 - Prob. 67ECh. R.3 - Prob. 68ECh. R.3 - Prob. 69ECh. R.3 - Prob. 70ECh. R.3 - Prob. 71ECh. R.3 - Prob. 72ECh. R.3 - Prob. 73ECh. R.3 - Prob. 74ECh. R.3 - Prob. 75ECh. R.3 - Prob. 76ECh. R.3 - Prob. 77ECh. R.3 - Prob. 78ECh. R.3 - Prob. 79ECh. R.3 - Prob. 80ECh. R.3 - Prob. 81ECh. R.3 - Prob. 82ECh. R.3 - Prob. 83ECh. R.3 - Prob. 84ECh. R.3 - Prob. 85ECh. R.3 - Prob. 86ECh. R.3 - Prob. 87ECh. R.3 - Prob. 88ECh. R.3 - Prob. 89ECh. R.3 - Prob. 90ECh. R.3 - Prob. 91ECh. R.3 - Prob. 92ECh. R.3 - Prob. 93ECh. R.3 - Prob. 94ECh. R.3 - Prob. 95ECh. R.3 - Prob. 96ECh. R.3 - Prob. 97ECh. R.3 - Prob. 98ECh. R.3 - Prob. 99ECh. R.3 - Prob. 100ECh. R.3 - Prob. 101ECh. R.3 - Prob. 102ECh. R.3 - Prob. 103ECh. R.3 - Prob. 104ECh. R.3 - Prob. 105ECh. R.3 - Prob. 106ECh. R.3 - Prob. 107ECh. R.3 - Prob. 108ECh. R.3 - Prob. 109ECh. R.3 - Prob. 110ECh. R.4 - Prob. 1ECh. R.4 - Prob. 2ECh. R.4 - Prob. 3ECh. R.4 - Prob. 4ECh. R.4 - Prob. 5ECh. R.4 - Prob. 6ECh. R.4 - Prob. 7ECh. R.4 - Prob. 8ECh. R.4 - Prob. 9ECh. R.4 - Prob. 10ECh. R.4 - Prob. 11ECh. R.4 - Prob. 12ECh. R.4 - Prob. 13ECh. R.4 - Prob. 14ECh. R.4 - Prob. 15ECh. R.4 - Prob. 16ECh. R.4 - Prob. 17ECh. R.4 - Prob. 18ECh. R.4 - Prob. 19ECh. R.4 - Prob. 20ECh. R.4 - Prob. 21ECh. R.4 - Prob. 22ECh. R.4 - Prob. 23ECh. R.4 - Prob. 24ECh. R.4 - Prob. 25ECh. R.4 - Prob. 26ECh. R.4 - Prob. 27ECh. R.4 - Prob. 28ECh. R.4 - Prob. 29ECh. R.4 - Prob. 30ECh. R.4 - Prob. 31ECh. R.4 - Prob. 32ECh. R.4 - Prob. 33ECh. R.4 - Prob. 34ECh. R.4 - Prob. 35ECh. R.4 - Prob. 36ECh. R.4 - Prob. 37ECh. R.4 - Prob. 38ECh. R.4 - Prob. 39ECh. R.4 - Prob. 40ECh. R.4 - Prob. 41ECh. R.4 - Prob. 42ECh. R.4 - Prob. 43ECh. R.4 - Prob. 44ECh. R.4 - Prob. 45ECh. R.4 - Prob. 46ECh. R.4 - Prob. 47ECh. R.4 - Prob. 48ECh. R.4 - Prob. 49ECh. R.4 - Prob. 50ECh. R.4 - Prob. 51ECh. R.4 - Prob. 52ECh. R.4 - Prob. 53ECh. R.4 - Prob. 54ECh. R.4 - Prob. 55ECh. R.4 - Prob. 56ECh. R.4 - Prob. 57ECh. R.4 - Prob. 58ECh. R.4 - Prob. 59ECh. R.4 - Prob. 60ECh. R.4 - Prob. 61ECh. R.4 - Prob. 62ECh. R.4 - Prob. 63ECh. R.4 - Prob. 64ECh. R.4 - Prob. 65ECh. R.4 - Prob. 66ECh. R.4 - Prob. 67ECh. R.4 - Prob. 68ECh. R.4 - Prob. 69ECh. R.4 - Prob. 70ECh. R.4 - Prob. 71ECh. R.4 - Prob. 72ECh. R.4 - Prob. 73ECh. R.4 - Prob. 74ECh. R.4 - Prob. 75ECh. R.4 - Prob. 76ECh. R.4 - Prob. 77ECh. R.4 - Prob. 78ECh. R.4 - Prob. 79ECh. R.4 - Prob. 80ECh. R.4 - Prob. 81ECh. R.4 - Prob. 82ECh. R.4 - Prob. 83ECh. R.4 - Prob. 84ECh. R.4 - Prob. 85ECh. R.4 - Prob. 86ECh. R.4 - Prob. 87ECh. R.4 - Prob. 88ECh. R.4 - Prob. 89ECh. R.4 - Prob. 90ECh. R.4 - Prob. 91ECh. R.4 - Prob. 92ECh. R.4 - Prob. 93ECh. R.4 - Prob. 94ECh. R.4 - Prob. 95ECh. R.4 - Prob. 96ECh. R.4 - Prob. 97ECh. R.4 - Prob. 98ECh. R.4 - Prob. 99ECh. R.4 - Prob. 100ECh. R.4 - Prob. 101ECh. R.4 - Prob. 102ECh. R.4 - Prob. 103ECh. R.4 - Prob. 104ECh. R.4 - Prob. 105ECh. R.4 - Prob. 106ECh. R.4 - Prob. 107ECh. R.4 - Prob. 108ECh. R.4 - Prob. 109ECh. R.4 - Prob. 110ECh. R.4 - Prob. 111ECh. R.4 - Prob. 112ECh. R.4 - Prob. 113ECh. R.4 - Prob. 114ECh. R.5 - Prob. 1ECh. R.5 - Prob. 2ECh. R.5 - Prob. 3ECh. R.5 - Prob. 4ECh. R.5 - Prob. 5ECh. R.5 - Prob. 6ECh. R.5 - Prob. 7ECh. R.5 - Prob. 8ECh. R.5 - Prob. 9ECh. R.5 - Prob. 10ECh. R.5 - Prob. 11ECh. R.5 - Prob. 12ECh. R.5 - Prob. 13ECh. R.5 - Prob. 14ECh. R.5 - Prob. 15ECh. R.5 - Prob. 16ECh. R.5 - Prob. 17ECh. R.5 - Prob. 18ECh. R.5 - Prob. 19ECh. R.5 - Prob. 20ECh. R.5 - Prob. 21ECh. R.5 - Prob. 22ECh. R.5 - Prob. 23ECh. R.5 - Prob. 24ECh. R.5 - Prob. 25ECh. R.5 - Prob. 26ECh. 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R.6 - Prob. 102ECh. R.6 - Prob. 103ECh. R.6 - Prob. 104ECh. R.6 - Prob. 105ECh. R.6 - Prob. 106ECh. R.6 - Prob. 107ECh. R.6 - Prob. 108ECh. R.6 - Prob. 109ECh. R.6 - Prob. 110ECh. R.6 - Prob. 111ECh. R.6 - Prob. 112ECh. R.6 - Prob. 113ECh. R.6 - Prob. 114ECh. R.6 - Prob. 115ECh. R.6 - Prob. 116ECh. R.7 - Prob. 1ECh. R.7 - Prob. 2ECh. R.7 - Prob. 3ECh. R.7 - Prob. 4ECh. R.7 - Prob. 5ECh. R.7 - Prob. 6ECh. R.7 - Prob. 7ECh. R.7 - Prob. 8ECh. R.7 - Prob. 9ECh. R.7 - Prob. 10ECh. R.7 - Prob. 11ECh. R.7 - Prob. 12ECh. R.7 - Prob. 13ECh. R.7 - Prob. 14ECh. R.7 - Prob. 15ECh. R.7 - Prob. 16ECh. R.7 - Prob. 17ECh. R.7 - Prob. 18ECh. R.7 - Prob. 19ECh. R.7 - Prob. 20ECh. R.7 - Prob. 21ECh. R.7 - Prob. 22ECh. R.7 - Prob. 23ECh. R.7 - Prob. 24ECh. R.7 - Prob. 25ECh. R.7 - Prob. 26ECh. R.7 - Prob. 27ECh. R.7 - Prob. 28ECh. R.7 - Prob. 29ECh. R.7 - Prob. 30ECh. R.7 - Prob. 31ECh. R.7 - Prob. 32ECh. R.7 - Prob. 33ECh. R.7 - Prob. 34ECh. R.7 - Prob. 35ECh. R.7 - Prob. 36ECh. R.7 - Prob. 37ECh. R.7 - Prob. 38ECh. R.7 - Prob. 39ECh. R.7 - Prob. 40ECh. R.7 - Prob. 41ECh. R.7 - Prob. 42ECh. R.7 - Prob. 43ECh. R.7 - Prob. 44ECh. R.7 - Prob. 45ECh. R.7 - Prob. 46ECh. R.7 - Prob. 47ECh. R.7 - Prob. 48ECh. R.7 - Prob. 49ECh. R.7 - Prob. 50ECh. R.7 - Prob. 51ECh. R.7 - Prob. 52ECh. R.7 - Prob. 53ECh. R.7 - Prob. 54ECh. R.7 - Prob. 55ECh. R.7 - Prob. 56ECh. R.7 - Prob. 57ECh. R.7 - Prob. 58ECh. R.7 - Prob. 59ECh. R.7 - Prob. 60ECh. R.7 - Prob. 61ECh. R.7 - Prob. 62ECh. R.7 - Prob. 63ECh. R.7 - Prob. 64ECh. R.7 - Prob. 65ECh. R.7 - Prob. 66ECh. R.7 - Prob. 67ECh. R.7 - Prob. 68ECh. R.7 - Prob. 69ECh. R.7 - Prob. 70ECh. R.7 - Prob. 71ECh. R.7 - Prob. 72ECh. R.7 - Prob. 73ECh. R.7 - Prob. 74ECh. R.7 - Prob. 75ECh. R.7 - Prob. 76ECh. R.7 - Prob. 77ECh. R.7 - Prob. 78ECh. R.7 - Prob. 79ECh. R.7 - Prob. 80ECh. R.7 - Prob. 81ECh. R.7 - Prob. 82ECh. R.7 - Prob. 83ECh. R.7 - Prob. 84ECh. R.7 - Prob. 85ECh. R.7 - Prob. 86ECh. R.7 - Prob. 87ECh. R.7 - Prob. 88ECh. R.7 - Prob. 89ECh. R.7 - Prob. 90ECh. R.7 - Prob. 91ECh. R.7 - Prob. 92ECh. R.7 - Prob. 93ECh. R.7 - Prob. 94ECh. R.7 - Prob. 95ECh. R.7 - Prob. 96ECh. R.7 - Prob. 97ECh. R.7 - Prob. 98ECh. R.7 - Prob. 99ECh. R.7 - Prob. 100ECh. R.7 - Prob. 101ECh. R.7 - Prob. 102ECh. R.7 - Prob. 103ECh. R.7 - Prob. 104ECh. R.7 - Prob. 105ECh. R.7 - Prob. 106ECh. R.7 - Prob. 107ECh. R.7 - Prob. 108ECh. R.7 - Prob. 109ECh. R.7 - Prob. 110ECh. R.7 - Prob. 111ECh. R.7 - Prob. 112ECh. R.7 - Prob. 113ECh. R.7 - Prob. 114ECh. R.7 - Prob. 115ECh. R.CR - Prob. 1CRCh. R.CR - Prob. 2CRCh. R.CR - Prob. 3CRCh. R.CR - Prob. 4CRCh. R.CR - Prob. 5CRCh. R.CR - Prob. 6CRCh. R.CR - Prob. 7CRCh. R.CR - Prob. 8CRCh. R.CR - Prob. 9CRCh. R.CR - Prob. 10CRCh. R.CR - Prob. 11CRCh. R.CR - Prob. 12CRCh. R.CR - Prob. 13CRCh. R.CR - Prob. 14CRCh. R.CR - Prob. 15CRCh. R.CR - Prob. 16CRCh. R.CR - Prob. 17CRCh. R.CR - Prob. 18CRCh. R.CR - Prob. 19CRCh. R.CR - Prob. 20CRCh. R.CR - Prob. 21CRCh. R.CR - Prob. 22CRCh. R.CR - Prob. 23CRCh. R.CR - Prob. 24CRCh. R.CR - Prob. 25CRCh. R.CR - Prob. 26CRCh. R.CR - Prob. 27CRCh. R.CR - Prob. 28CRCh. R.CR - Prob. 29CRCh. R.CR - Prob. 30CRCh. R.CR - Prob. 31CRCh. R.CR - Prob. 32CRCh. R.CR - Prob. 33CRCh. R.CR - Prob. 34CRCh. R.CR - Prob. 35CRCh. R.CR - Prob. 36CRCh. R.CR - Prob. 37CRCh. R.CR - Prob. 38CRCh. R.CR - Prob. 39CRCh. R.CR - Prob. 40CRCh. R.CR - Prob. 41CRCh. R.CR - Prob. 42CRCh. R.CR - Prob. 43CRCh. R.CR - Prob. 44CRCh. R.CR - Prob. 45CRCh. R.CR - Prob. 46CRCh. R.CR - Prob. 47CRCh. R.CR - Prob. 48CRCh. R.CR - Prob. 49CRCh. R.CR - Prob. 50CRCh. R.CR - Prob. 51CRCh. R.CR - Prob. 52CRCh. R.CR - Prob. 53CRCh. R.CR - Prob. 54CRCh. R.CR - Prob. 55CRCh. R.CR - Prob. 56CRCh. R.CR - Prob. 57CRCh. R.CR - Prob. 58CRCh. R.CR - Prob. 59CRCh. R.CR - Prob. 60CRCh. R.CR - Prob. 61CRCh. R.CR - Prob. 62CRCh. R.CR - Prob. 63CRCh. R.CR - Prob. 64CRCh. R.CR - Prob. 65CRCh. R.CR - Prob. 66CRCh. R.CR - Prob. 67CRCh. R.CR - Prob. 68CRCh. R.CR - Prob. 69CRCh. R.CR - Prob. 70CRCh. R.CR - Prob. 71CRCh. R.CR - Prob. 72CRCh. R.CR - Prob. 73CRCh. R.CR - Prob. 74CRCh. R.CR - Prob. 75CRCh. R.CR - Prob. 76CRCh. R.CR - Prob. 77CRCh. R.CR - Prob. 78CRCh. R.CR - Prob. 79CRCh. R.CR - Prob. 80CRCh. R.CR - Prob. 81CRCh. R.CR - Prob. 82CRCh. R.CR - Prob. 83CRCh. R.CR - Prob. 84CRCh. R.CR - Prob. 85CRCh. R.CR - Prob. 86CRCh. R.CR - Prob. 87CRCh. R.CR - Prob. 88CRCh. R.CR - Prob. 89CRCh. R.CR - Prob. 90CRCh. R.CR - Prob. 91CRCh. R.CR - Prob. 92CRCh. R.CR - Prob. 93CRCh. R.CR - Prob. 94CRCh. R.CR - Prob. 95CRCh. R.CR - Prob. 96CRCh. R.CR - Prob. 97CRCh. R.CR - Prob. 98CRCh. R.CR - Prob. 99CRCh. R.CR - Prob. 100CRCh. R.CR - Prob. 101CRCh. R.CR - Prob. 102CRCh. R.CR - Prob. 103CRCh. R.CR - Prob. 104CRCh. R.CR - Prob. 105CRCh. R.CR - Prob. 106CRCh. R.CR - Prob. 107CRCh. R.CR - Prob. 108CRCh. R.CR - Prob. 109CRCh. R.CR - Prob. 110CRCh. R.CR - Prob. 111CRCh. R.CR - Prob. 112CRCh. R.CR - Prob. 113CRCh. R.CR - Prob. 114CRCh. R.CR - Prob. 115CRCh. R.CR - Prob. 116CRCh. R.CR - Prob. 117CRCh. R.CR - Prob. 118CRCh. R.CR - Prob. 119CRCh. R.CR - Prob. 120CRCh. R.CR - Prob. 121CRCh. R.CR - Prob. 122CRCh. R.CR - Prob. 123CRCh. R.CR - Prob. 124CRCh. R.CR - Prob. 125CRCh. R.CT - Prob. 1CTCh. R.CT - Prob. 2CTCh. R.CT - Prob. 3CTCh. R.CT - Prob. 4CTCh. R.CT - Prob. 5CTCh. R.CT - Prob. 6CTCh. R.CT - Prob. 7CTCh. R.CT - Prob. 8CTCh. R.CT - Prob. 9CTCh. R.CT - Prob. 10CTCh. R.CT - Prob. 11CTCh. R.CT - Prob. 12CTCh. R.CT - Prob. 13CTCh. R.CT - Prob. 14CTCh. R.CT - Prob. 15CTCh. R.CT - Prob. 16CTCh. R.CT - Prob. 17CTCh. R.CT - Prob. 18CTCh. R.CT - Prob. 19CTCh. R.CT - Prob. 20CTCh. R.CT - Prob. 21CTCh. R.CT - Prob. 22CTCh. R.CT - Prob. 23CTCh. R.CT - Prob. 24CTCh. R.CT - Prob. 25CTCh. R.CT - Prob. 26CTCh. R.CT - Prob. 27CTCh. R.CT - Prob. 28CTCh. R.CT - Prob. 29CTCh. R.CT - Prob. 30CTCh. R.CT - Prob. 31CTCh. R.CT - Prob. 32CT
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