(a) Answer The value of A + B is [ − 4 9 1 5 − 6 − 5 15 − 5 − 2 3 10 − 10 − 4 − 2 − 2 ] . Explanation Given: The matrices A = [ − 1 4 0 3 − 2 2 5 4 − 1 0 8 − 6 − 4 − 1 0 ] and B = [ − 3 5 1 2 − 4 − 7 10 − 9 − 1 3 2 − 4 0 − 1 − 2 ] . Concept used: Operations like addition and subtraction of matrices are only possible when they are of same dimension. Dimension of matrix with a rows and b columns is given by a × b . If a matrix is multiplied by a scalar then each element of the matrix is multiplied by the same scalar. Calculation: Add the matrix A and Bas follows: A + B = [ − 1 4 0 3 − 2 2 5 4 − 1 0 8 − 6 − 4 − 1 0 ] + [ − 3 5 1 2 − 4 − 7 10 − 9 − 1 3 2 − 4 0 − 1 − 2 ] = [ − 1 − 3 4 + 5 1 + 0 3 + 2 − 2 − 4 2 − 7 5 + 10 4 − 9 − 1 − 1 0 + 3 8 + 2 − 6 − 4 − 4 + 0 − 1 − 1 0 − 2 ] = [ − 4 9 1 5 − 6 − 5 15 − 5 − 2 3 10 − 10 − 4 − 2 − 2 ] Thus, the value of A + B is [ − 4 9 1 5 − 6 − 5 15 − 5 − 2 3 10 − 10 − 4 − 2 − 2 ] . Now, by graphing utility of matrix capability, Hence, the result is verified. (b) To determine To find A − B and check your result by graphing utility. Answer The value of A − B is [ − 2 − 1 − 1 1 2 9 − 5 13 0 3 6 − 2 − 4 0 2 ] . Explanation Given: The matrices A = [ − 1 4 0 3 − 2 2 5 4 − 1 0 8 − 6 − 4 − 1 0 ] and B = [ − 3 5 1 2 − 4 − 7 10 − 9 − 1 3 2 − 4 0 − 1 − 2 ] . Concept used: Operations like addition and subtraction of matrices are only possible when they are of same dimension. Dimension of matrix with a rows and b columns is given by a × b . If a matrix is multiplied by a scalar then each element of the matrix is multiplied by the same scalar. Calculation: Subtract the matrices A and Bas follows: A − B = [ − 1 4 0 3 − 2 2 5 4 − 1 0 8 − 6 − 4 − 1 0 ] − [ − 3 5 1 2 − 4 − 7 10 − 9 − 1 3 2 − 4 0 − 1 − 2 ] = [ − 1 + 3 4 − 5 0 − 1 3 − 2 − 2 + 4 2 + 7 5 − 10 4 + 9 − 1 + 1 0 + 3 8 − 2 − 6 + 4 − 4 − 0 − 1 + 1 0 + 2 ] = [ − 2 − 1 − 1 1 2 9 − 5 13 0 3 6 − 2 − 4 0 2 ] Thus, the value of A − B is [ − 2 − 1 − 1 1 2 9 − 5 13 0 3 6 − 2 − 4 0 2 ] . Now, by graphing utility of matrix capability, Hence, the result is verified. (c) To determine To find 3 A and check your result by graphing utility. Answer The value of 3 A is [ − 3 12 0 9 − 6 6 15 12 − 3 0 24 − 18 − 12 − 3 0 ] . Explanation Given: The matrix is A = [ − 1 4 0 3 − 2 2 5 4 − 1 0 8 − 6 − 4 − 1 0 ] . Concept used: Operations like addition and subtraction of matrices are only possible when they are of same dimension. Dimension of matrix with a rows and b columns is given by a × b . If a matrix is multiplied by a scalar then each element of the matrix is multiplied by the same scalar. Calculation: Multiply all the elements of matrix A by 3 as follows: 3 A = 3 [ − 1 4 0 3 − 2 2 5 4 − 1 0 8 − 6 − 4 − 1 0 ] = [ − 3 12 0 9 − 6 6 15 12 − 3 0 24 − 18 − 12 − 3 0 ] Thus, the value of 3 A is [ − 3 12 0 9 − 6 6 15 12 − 3 0 24 − 18 − 12 − 3 0 ] . Now, by graphing utility of matrix capability, Hence, the result is verified. (d) To determine To find 3 A − 2 B and check your result by graphing utility. Answer The value of 3 A − 2 B is [ 3 2 − 2 5 2 20 − 5 30 − 1 − 6 20 − 10 − 12 − 1 4 ] . Explanation Given: The matrices A = [ − 1 4 0 3 − 2 2 5 4 − 1 0 8 − 6 − 4 − 1 0 ] and B = [ − 3 5 1 2 − 4 − 7 10 − 9 − 1 3 2 − 4 0 − 1 − 2 ] . Concept used: Operations like addition and subtraction of matrices are only possible when they are of same dimension. Dimension of matrix with a rows and b columns is given by a × b . If a matrix is multiplied by a scalar then each element of the matrix is multiplied by the same scalar. Calculation: The value of 3 A − 2 B is calculated as follows: Thus, the value of 3 A − 2 B is [ 3 2 − 2 5 2 20 − 5 30 − 1 − 6 20 − 10 − 12 − 1 4 ] . Now, by graphing utility of matrix capability, Hence, the result is verified.

8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

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Question

Chapter 7.5, Problem 18E

(a)

To determine

To find A+B and check your result by graphingutility.

(a)

Expert Solution

Answer to Problem 18E

The value of A+B is [−4915−6−515−5−2310−10−4−2−2] .

Explanation of Solution

Given:

The matrices A=[−1403−2254−108−6−4−10] and B=[−3512−4−710−9−132−40−1−2] .

Concept used:

Operations like addition and subtraction of matrices are only possible when they are of same dimension.

Dimension of matrix with a rows and b columns is given by a×b .

If a matrix is multiplied by a scalar then each element of the matrix is multiplied by the same scalar.

Calculation:

Add the matrix A and Bas follows:

A+B=[−1403−2254−108−6−4−10]+[−3512−4−710−9−132−40−1−2]=[−1−34+51+03+2−2−42−75+104−9−1−10+38+2−6−4−4+0−1−10−2]=[−4915−6−515−5−2310−10−4−2−2]

Thus, the value of A+B is [−4915−6−515−5−2310−10−4−2−2] .

Now, by graphing utility of matrix capability,

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 7.5, Problem 18E , additional homework tip 1

Hence, the result is verified.

(b)

To determine

To find A−B and check your result by graphing utility.

(b)

Expert Solution

Answer to Problem 18E

The value of A−B is [−2−1−1129−513036−2−402] .

Explanation of Solution

Given:

The matrices A=[−1403−2254−108−6−4−10] and B=[−3512−4−710−9−132−40−1−2] .

Concept used:

Operations like addition and subtraction of matrices are only possible when they are of same dimension.

Dimension of matrix with a rows and b columns is given by a×b .

If a matrix is multiplied by a scalar then each element of the matrix is multiplied by the same scalar.

Calculation:

Subtract the matrices A and Bas follows:

A−B=[−1403−2254−108−6−4−10]−[−3512−4−710−9−132−40−1−2]=[−1+34−50−13−2−2+42+75−104+9−1+10+38−2−6+4−4−0−1+10+2]=[−2−1−1129−513036−2−402]

Thus, the value of A−B is [−2−1−1129−513036−2−402] .

Now, by graphing utility of matrix capability,

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 7.5, Problem 18E , additional homework tip 2

Hence, the result is verified.

(c)

To determine

To find 3A and check your result by graphing utility.

(c)

Expert Solution

Answer to Problem 18E

The value of 3A is [−31209−661512−3024−18−12−30] .

Explanation of Solution

Given:

The matrix is A=[−1403−2254−108−6−4−10] .

Concept used:

Operations like addition and subtraction of matrices are only possible when they are of same dimension.

Dimension of matrix with a rows and b columns is given by a×b .

If a matrix is multiplied by a scalar then each element of the matrix is multiplied by the same scalar.

Calculation:

Multiply all the elements of matrix A by 3 as follows:

3A=3[−1403−2254−108−6−4−10]=[−31209−661512−3024−18−12−30]

Thus, the value of 3A is [−31209−661512−3024−18−12−30] .

Now, by graphing utility of matrix capability,

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 7.5, Problem 18E , additional homework tip 3

Hence, the result is verified.

(d)

To determine

To find 3A−2B and check your result by graphing utility.

(d)

Expert Solution

Answer to Problem 18E

The value of 3A−2B is [32−25220−530−1−620−10−12−14] .

Explanation of Solution

Given:

The matrices A=[−1403−2254−108−6−4−10] and B=[−3512−4−710−9−132−40−1−2] .

Concept used:

Operations like addition and subtraction of matrices are only possible when they are of same dimension.

Dimension of matrix with a rows and b columns is given by a×b .

If a matrix is multiplied by a scalar then each element of the matrix is multiplied by the same scalar.

Calculation:

The value of 3A−2B is calculated as follows:

Thus, the value of 3A−2B is [32−25220−530−1−620−10−12−14] .

Now, by graphing utility of matrix capability,

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS), Chapter 7.5, Problem 18E , additional homework tip 4

Hence, the result is verified.

Chapter 7.5, Problem 17E

Chapter 7.5, Problem 19E

Chapter 7 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

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Prob. 77E Ch. 7.5 - Prob. 78E Ch. 7.5 - Prob. 79E Ch. 7.5 - Prob. 80E Ch. 7.5 - Prob. 81E Ch. 7.5 - Prob. 82E Ch. 7.5 - Prob. 83E Ch. 7.5 - Prob. 84E Ch. 7.5 - Prob. 85E Ch. 7.5 - Prob. 86E Ch. 7.5 - Prob. 87E Ch. 7.5 - Prob. 88E Ch. 7.5 - Prob. 89E Ch. 7.5 - Prob. 90E Ch. 7.5 - Prob. 91E Ch. 7.5 - Prob. 92E Ch. 7.5 - Prob. 93E Ch. 7.5 - Prob. 94E Ch. 7.5 - Prob. 95E Ch. 7.5 - Prob. 96E Ch. 7.5 - Prob. 97E Ch. 7.5 - Prob. 98E Ch. 7.5 - Prob. 99E Ch. 7.5 - Prob. 100E Ch. 7.5 - Prob. 101E Ch. 7.5 - Prob. 102E Ch. 7.5 - Prob. 103E Ch. 7.5 - Prob. 104E Ch. 7.5 - Prob. 105E Ch. 7.5 - Prob. 106E Ch. 7.5 - Prob. 107E Ch. 7.5 - Prob. 108E Ch. 7.5 - Prob. 109E Ch. 7.5 - Prob. 110E Ch. 7.5 - Prob. 111E Ch. 7.5 - Prob. 112E Ch. 7.5 - Prob. 113E Ch. 7.5 - Prob. 114E Ch. 7.5 - Prob. 115E Ch. 7.5 - Prob. 116E Ch. 7.5 - Prob. 117E Ch. 7.5 - Prob. 118E Ch. 7.5 - Prob. 119E Ch. 7.5 - Prob. 120E Ch. 7.6 - Prob. 1E Ch. 7.6 - Prob. 2E Ch. 7.6 - Prob. 3E Ch. 7.6 - Prob. 4E Ch. 7.6 - Prob. 5E Ch. 7.6 - Prob. 6E Ch. 7.6 - Prob. 7E Ch. 7.6 - Prob. 8E Ch. 7.6 - Prob. 9E Ch. 7.6 - Prob. 10E Ch. 7.6 - Prob. 11E Ch. 7.6 - Prob. 12E Ch. 7.6 - Prob. 13E Ch. 7.6 - Prob. 14E Ch. 7.6 - Prob. 15E Ch. 7.6 - Prob. 16E Ch. 7.6 - Prob. 17E Ch. 7.6 - Prob. 18E Ch. 7.6 - Prob. 19E Ch. 7.6 - Prob. 20E Ch. 7.6 - Prob. 21E Ch. 7.6 - Prob. 22E Ch. 7.6 - Prob. 23E Ch. 7.6 - Prob. 24E Ch. 7.6 - Prob. 25E Ch. 7.6 - Prob. 26E Ch. 7.6 - Prob. 27E Ch. 7.6 - Prob. 28E Ch. 7.6 - Prob. 29E Ch. 7.6 - Prob. 30E Ch. 7.6 - Prob. 31E Ch. 7.6 - Prob. 32E Ch. 7.6 - Prob. 33E Ch. 7.6 - Prob. 34E Ch. 7.6 - Prob. 35E Ch. 7.6 - Prob. 36E Ch. 7.6 - Prob. 37E Ch. 7.6 - Prob. 38E Ch. 7.6 - Prob. 39E Ch. 7.6 - Prob. 40E Ch. 7.6 - Prob. 41E Ch. 7.6 - Prob. 42E Ch. 7.6 - Prob. 43E Ch. 7.6 - Prob. 44E Ch. 7.6 - Prob. 45E Ch. 7.6 - Prob. 46E Ch. 7.6 - Prob. 47E Ch. 7.6 - Prob. 48E Ch. 7.6 - Prob. 49E Ch. 7.6 - Prob. 50E Ch. 7.6 - Prob. 51E Ch. 7.6 - Prob. 52E Ch. 7.6 - Prob. 53E Ch. 7.6 - Prob. 54E Ch. 7.6 - Prob. 55E Ch. 7.6 - Prob. 56E Ch. 7.6 - Prob. 57E Ch. 7.6 - Prob. 58E Ch. 7.6 - Prob. 59E Ch. 7.6 - Prob. 60E Ch. 7.6 - Prob. 61E Ch. 7.6 - Prob. 62E Ch. 7.6 - Prob. 64E Ch. 7.6 - Prob. 65E Ch. 7.6 - Prob. 66E Ch. 7.6 - Prob. 67E Ch. 7.6 - Prob. 68E Ch. 7.6 - Prob. 69E Ch. 7.6 - Prob. 70E Ch. 7.6 - Prob. 71E Ch. 7.6 - Prob. 72E Ch. 7.6 - Prob. 73E Ch. 7.6 - Prob. 74E Ch. 7.6 - Prob. 75E Ch. 7.6 - Prob. 76E Ch. 7.7 - Prob. 1E Ch. 7.7 - Prob. 2E Ch. 7.7 - Prob. 3E Ch. 7.7 - Prob. 4E Ch. 7.7 - Prob. 5E Ch. 7.7 - Prob. 6E Ch. 7.7 - Prob. 7E Ch. 7.7 - Prob. 8E Ch. 7.7 - Prob. 9E Ch. 7.7 - Prob. 10E Ch. 7.7 - Prob. 11E Ch. 7.7 - Prob. 12E Ch. 7.7 - Prob. 13E Ch. 7.7 - Prob. 14E Ch. 7.7 - Prob. 15E Ch. 7.7 - Prob. 16E Ch. 7.7 - Prob. 17E Ch. 7.7 - Prob. 18E Ch. 7.7 - Prob. 19E Ch. 7.7 - Prob. 20E Ch. 7.7 - Prob. 21E Ch. 7.7 - Prob. 22E Ch. 7.7 - Prob. 23E Ch. 7.7 - Prob. 24E Ch. 7.7 - Prob. 25E Ch. 7.7 - Prob. 26E Ch. 7.7 - Prob. 27E Ch. 7.7 - Prob. 28E Ch. 7.7 - Prob. 29E Ch. 7.7 - Prob. 30E Ch. 7.7 - Prob. 31E Ch. 7.7 - Prob. 32E Ch. 7.7 - Prob. 33E Ch. 7.7 - Prob. 34E Ch. 7.7 - Prob. 35E Ch. 7.7 - Prob. 36E Ch. 7.7 - Prob. 37E Ch. 7.7 - Prob. 38E Ch. 7.7 - Prob. 39E Ch. 7.7 - Prob. 40E Ch. 7.7 - Prob. 41E Ch. 7.7 - Prob. 42E Ch. 7.7 - Prob. 43E Ch. 7.7 - Prob. 44E Ch. 7.7 - Prob. 45E Ch. 7.7 - Prob. 46E Ch. 7.7 - Prob. 47E Ch. 7.7 - Prob. 48E Ch. 7.7 - Prob. 49E Ch. 7.7 - Prob. 50E Ch. 7.7 - Prob. 51E Ch. 7.7 - Prob. 52E Ch. 7.7 - Prob. 53E Ch. 7.7 - Prob. 54E Ch. 7.7 - Prob. 55E Ch. 7.7 - Prob. 56E Ch. 7.7 - Prob. 57E Ch. 7.7 - Prob. 58E Ch. 7.7 - Prob. 59E Ch. 7.7 - Prob. 60E Ch. 7.7 - Prob. 61E Ch. 7.7 - Prob. 62E Ch. 7.7 - Prob. 63E Ch. 7.7 - Prob. 64E Ch. 7.7 - Prob. 65E Ch. 7.7 - Prob. 66E Ch. 7.7 - Prob. 67E Ch. 7.7 - Prob. 68E Ch. 7.7 - Prob. 69E Ch. 7.7 - Prob. 70E Ch. 7.7 - Prob. 71E Ch. 7.7 - Prob. 72E Ch. 7.7 - Prob. 73E Ch. 7.7 - Prob. 74E Ch. 7.7 - Prob. 75E Ch. 7.7 - Prob. 76E Ch. 7.7 - Prob. 77E Ch. 7.7 - Prob. 78E Ch. 7.7 - Prob. 79E Ch. 7.7 - Prob. 80E Ch. 7.7 - Prob. 81E Ch. 7.7 - Prob. 82E Ch. 7.7 - Prob. 83E Ch. 7.7 - Prob. 84E Ch. 7.7 - Prob. 85E Ch. 7.7 - Prob. 86E Ch. 7.7 - Prob. 87E Ch. 7.7 - Prob. 88E Ch. 7.8 - Prob. 1E Ch. 7.8 - Prob. 2E Ch. 7.8 - Prob. 3E Ch. 7.8 - Prob. 4E Ch. 7.8 - Prob. 5E Ch. 7.8 - Prob. 6E Ch. 7.8 - Prob. 7E Ch. 7.8 - Prob. 8E Ch. 7.8 - Prob. 9E Ch. 7.8 - Prob. 10E Ch. 7.8 - Prob. 11E Ch. 7.8 - Prob. 12E Ch. 7.8 - Prob. 13E Ch. 7.8 - Prob. 14E Ch. 7.8 - Prob. 15E Ch. 7.8 - Prob. 16E Ch. 7.8 - Prob. 17E Ch. 7.8 - Prob. 18E Ch. 7.8 - Prob. 19E Ch. 7.8 - Prob. 20E Ch. 7.8 - Prob. 21E Ch. 7.8 - Prob. 22E Ch. 7.8 - Prob. 23E Ch. 7.8 - Prob. 24E Ch. 7.8 - Prob. 25E Ch. 7.8 - Prob. 26E Ch. 7.8 - Prob. 27E Ch. 7.8 - Prob. 28E Ch. 7.8 - Prob. 29E Ch. 7.8 - Prob. 30E Ch. 7.8 - Prob. 31E Ch. 7.8 - Prob. 32E Ch. 7.8 - Prob. 33E Ch. 7.8 - Prob. 34E Ch. 7.8 - Prob. 35E Ch. 7.8 - Prob. 36E Ch. 7.8 - Prob. 41E Ch. 7.8 - Prob. 42E Ch. 7.8 - Prob. 43E Ch. 7.8 - Prob. 44E Ch. 7.8 - Prob. 45E Ch. 7.8 - Prob. 46E Ch. 7.8 - Prob. 47E Ch. 7.8 - Prob. 48E Ch. 7 - Prob. 1CR Ch. 7 - Prob. 2CR Ch. 7 - Prob. 3CR Ch. 7 - Prob. 4CR Ch. 7 - Prob. 5CR Ch. 7 - Prob. 6CR Ch. 7 - Prob. 7CR Ch. 7 - Prob. 8CR Ch. 7 - Prob. 9CR Ch. 7 - Prob. 10CR Ch. 7 - Prob. 11CR Ch. 7 - Prob. 12CR Ch. 7 - Prob. 13CR Ch. 7 - Prob. 14CR Ch. 7 - Prob. 15CR Ch. 7 - Prob. 16CR Ch. 7 - Prob. 17CR Ch. 7 - Prob. 18CR Ch. 7 - Prob. 19CR Ch. 7 - Prob. 20CR Ch. 7 - Prob. 21CR Ch. 7 - Prob. 22CR Ch. 7 - Prob. 23CR Ch. 7 - Prob. 24CR Ch. 7 - Prob. 25CR Ch. 7 - Prob. 26CR Ch. 7 - Prob. 27CR Ch. 7 - Prob. 28CR Ch. 7 - Prob. 29CR Ch. 7 - Prob. 30CR Ch. 7 - Prob. 31CR Ch. 7 - Prob. 32CR Ch. 7 - Prob. 33CR Ch. 7 - Prob. 34CR Ch. 7 - Prob. 35CR Ch. 7 - Prob. 36CR Ch. 7 - Prob. 37CR Ch. 7 - Prob. 38CR Ch. 7 - Prob. 39CR Ch. 7 - Prob. 40CR Ch. 7 - Prob. 41CR Ch. 7 - Prob. 42CR Ch. 7 - Prob. 43CR Ch. 7 - Prob. 44CR Ch. 7 - Prob. 45CR Ch. 7 - Prob. 46CR Ch. 7 - Prob. 47CR Ch. 7 - Prob. 48CR Ch. 7 - Prob. 49CR Ch. 7 - Prob. 50CR Ch. 7 - Prob. 51CR Ch. 7 - Prob. 52CR Ch. 7 - Prob. 53CR Ch. 7 - Prob. 54CR Ch. 7 - Prob. 55CR Ch. 7 - Prob. 56CR Ch. 7 - Prob. 57CR Ch. 7 - Prob. 58CR Ch. 7 - Prob. 59CR Ch. 7 - Prob. 60CR Ch. 7 - Prob. 61CR Ch. 7 - Prob. 62CR Ch. 7 - Prob. 63CR Ch. 7 - Prob. 64CR Ch. 7 - Prob. 65CR Ch. 7 - Prob. 66CR Ch. 7 - Prob. 67CR Ch. 7 - Prob. 68CR Ch. 7 - Prob. 69CR Ch. 7 - Prob. 70CR Ch. 7 - Prob. 71CR Ch. 7 - Prob. 72CR Ch. 7 - Prob. 73CR Ch. 7 - Prob. 74CR Ch. 7 - Prob. 75CR Ch. 7 - Prob. 76CR Ch. 7 - Prob. 77CR Ch. 7 - Prob. 78CR Ch. 7 - Prob. 79CR Ch. 7 - Prob. 80CR Ch. 7 - Prob. 81CR Ch. 7 - Prob. 82CR Ch. 7 - Prob. 83CR Ch. 7 - Prob. 84CR Ch. 7 - Prob. 85CR Ch. 7 - Prob. 86CR Ch. 7 - Prob. 87CR Ch. 7 - Prob. 88CR Ch. 7 - Prob. 89CR Ch. 7 - Prob. 90CR Ch. 7 - Prob. 91CR Ch. 7 - Prob. 92CR Ch. 7 - Prob. 93CR Ch. 7 - Prob. 94CR Ch. 7 - Prob. 95CR Ch. 7 - Prob. 96CR Ch. 7 - Prob. 97CR Ch. 7 - Prob. 98CR Ch. 7 - Prob. 99CR Ch. 7 - Prob. 100CR Ch. 7 - Prob. 101CR Ch. 7 - Prob. 102CR Ch. 7 - Prob. 103CR Ch. 7 - Prob. 104CR Ch. 7 - Prob. 105CR Ch. 7 - Prob. 106CR Ch. 7 - Prob. 107CR Ch. 7 - Prob. 108CR Ch. 7 - Prob. 109CR Ch. 7 - Prob. 110CR Ch. 7 - Prob. 111CR Ch. 7 - Prob. 112CR Ch. 7 - Prob. 113CR Ch. 7 - Prob. 114CR Ch. 7 - Prob. 115CR Ch. 7 - Prob. 116CR Ch. 7 - Prob. 117CR Ch. 7 - Prob. 118CR Ch. 7 - Prob. 119CR Ch. 7 - Prob. 120CR Ch. 7 - Prob. 121CR Ch. 7 - Prob. 122CR Ch. 7 - Prob. 123CR Ch. 7 - Prob. 124CR Ch. 7 - Prob. 125CR Ch. 7 - Prob. 126CR Ch. 7 - Prob. 127CR Ch. 7 - Prob. 128CR Ch. 7 - Prob. 129CR Ch. 7 - Prob. 130CR Ch. 7 - Prob. 131CR Ch. 7 - Prob. 132CR Ch. 7 - Prob. 133CR Ch. 7 - Prob. 134CR Ch. 7 - Prob. 135CR Ch. 7 - Prob. 136CR Ch. 7 - Prob. 137CR Ch. 7 - Prob. 138CR Ch. 7 - Prob. 139CR Ch. 7 - Prob. 140CR Ch. 7 - Prob. 141CR Ch. 7 - Prob. 1CT Ch. 7 - Prob. 2CT Ch. 7 - Prob. 3CT Ch. 7 - Prob. 4CT Ch. 7 - Prob. 5CT Ch. 7 - Prob. 6CT Ch. 7 - Prob. 7CT Ch. 7 - Prob. 8CT Ch. 7 - Prob. 9CT Ch. 7 - Prob. 10CT Ch. 7 - Prob. 11CT Ch. 7 - Prob. 12CT Ch. 7 - Prob. 13CT Ch. 7 - Prob. 14CT Ch. 7 - Prob. 15CT Ch. 7 - Prob. 16CT Ch. 7 - Prob. 17CT

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