Glencoe Algebra 2 Student Edition C2014
Glencoe Algebra 2 Student Edition C2014
1st Edition
ISBN: 9780076639908
Author: McGraw-Hill Glencoe
Publisher: MCG
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Chapter 3.5, Problem 34HP

(a)

To determine

To explain: Whether the statement is sometimes , always , or never true for the matrices A and B .

(a)

Expert Solution
Check Mark

Answer to Problem 34HP

The statement is always true.

Explanation of Solution

Given information:

If A+B exists,

Then

  A−B exists.

According to the statement,

If A+B exists,

That means

The dimensions of the two matrices are the same.

Thus,

As long as the dimensions of the matrices are the same,

If A+B exists,

Then

  A−B alwaysexists .

(b)

To determine

To explain: Whether the statement isalways , sometimes , or never true for the matrices A and B .

(b)

Expert Solution
Check Mark

Answer to Problem 34HP

The statement is always true.

Explanation of Solution

Given information:

If k is a real number,

Then

kA and kB exist.

In this case,

k acts as a scalar.

According to the statement,

If k is a real number,

We can apply it to any of the matrices,

Either A or B .

Therefore,

The statement is always true.

(c)

To determine

To explain: Whether the statement is never , sometimes , or always true for the matrices A and B .

(c)

Expert Solution
Check Mark

Answer to Problem 34HP

The statement is always true.

Explanation of Solution

Given information:

If A−B does not exist,

Then

  B−A does not exist.

According to the statement,

If A−B does not exist,

That only means

The dimensions of the two matrices are not the same.

Thus,

As long as the dimensions of the matrices are not the same,

If A−B does not exist,

Then

  B−A alwaysdoes not exist.

(d)

To determine

To explain: Whether the statement is always , never , or sometimes true for the matrices A and B .

(d)

Expert Solution
Check Mark

Answer to Problem 34HP

The statement is sometimes true.

Explanation of Solution

Given information:

If A and B have the same number of elements,

Then

  A+B exists.

A and B may have the same number of elements,

Such that

That does not necessarily mean that both A and B have the same dimensions.

For example:

A could be 2×3 matrix.

Whereas,

B could be 1×6 matrix.

Both matrices have 6 elements,

But the dimensions are different.

Hence,

We could not add them together.

Therefore,

The statement is sometimes true.

Since it is possible that both matrices A and B could have the same dimensions and could be added together.

Thus,

We can say that

The statement is sometimes true.

(e)

To determine

To explain: Whether the statement isnever , always , or sometimestrue for the matrices A and B .

(e)

Expert Solution
Check Mark

Answer to Problem 34HP

The statement is sometimes true.

Explanation of Solution

Given information:

If kA exists and kB exists,

Then

  kA+kB exists.

We know that

kA exists and kB exists,

That means

Both matrices A and B have the scalar k .

However,

We don’t know the dimensions of either matrix.

Thus,

We cannot say for sure that kA+kB exists.

Therefore,

The statement is sometimes true.

Sometimes refers to that the matrices could have the same dimensions, which would allow them to be added together.

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Chapter 3.5, Problem 33HP
Next
Chapter 3.5, Problem 35HP

Chapter 3 Solutions

Glencoe Algebra 2 Student Edition C2014

Ch. 3.1 - Prob. 1ECh. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
Ch. 3.1 - Prob. 1AGPCh. 3.1 - Prob. 1BGPCh. 3.1 - Prob. 2AGPCh. 3.1 - Prob. 2BGPCh. 3.1 - Prob. 3AGPCh. 3.1 - Prob. 3BGPCh. 3.1 - Prob. 4AGPCh. 3.1 - Prob. 4BGPCh. 3.1 - Prob. 4CGPCh. 3.1 - Prob. 5AGPCh. 3.1 - Prob. 5BGPCh. 3.1 - Prob. 5CGPCh. 3.1 - Prob. 6GPCh. 3.1 - Prob. 1CYUCh. 3.1 - Prob. 2CYUCh. 3.1 - Prob. 3CYUCh. 3.1 - Prob. 4CYUCh. 3.1 - Prob. 5CYUCh. 3.1 - Prob. 6CYUCh. 3.1 - Prob. 7CYUCh. 3.1 - Prob. 8CYUCh. 3.1 - Prob. 9CYUCh. 3.1 - Prob. 10CYUCh. 3.1 - Prob. 11CYUCh. 3.1 - Prob. 12CYUCh. 3.1 - Prob. 13CYUCh. 3.1 - Prob. 14CYUCh. 3.1 - Prob. 15CYUCh. 3.1 - Prob. 16CYUCh. 3.1 - Prob. 17CYUCh. 3.1 - Prob. 18CYUCh. 3.1 - Prob. 19CYUCh. 3.1 - Prob. 20CYUCh. 3.1 - Prob. 21CYUCh. 3.1 - Prob. 22CYUCh. 3.1 - Prob. 23CYUCh. 3.1 - Prob. 24CYUCh. 3.1 - Prob. 25CYUCh. 3.1 - Prob. 26PPSCh. 3.1 - Prob. 27PPSCh. 3.1 - Prob. 28PPSCh. 3.1 - Prob. 29PPSCh. 3.1 - Prob. 30PPSCh. 3.1 - Prob. 31PPSCh. 3.1 - Prob. 32PPSCh. 3.1 - Prob. 33PPSCh. 3.1 - Prob. 34PPSCh. 3.1 - Prob. 35PPSCh. 3.1 - Prob. 36PPSCh. 3.1 - Prob. 37PPSCh. 3.1 - Prob. 38PPSCh. 3.1 - Prob. 39PPSCh. 3.1 - Prob. 40PPSCh. 3.1 - Prob. 41PPSCh. 3.1 - Prob. 42PPSCh. 3.1 - Prob. 43PPSCh. 3.1 - Prob. 44PPSCh. 3.1 - Prob. 45PPSCh. 3.1 - Prob. 46PPSCh. 3.1 - Prob. 47PPSCh. 3.1 - Prob. 48PPSCh. 3.1 - Prob. 49PPSCh. 3.1 - Prob. 50PPSCh. 3.1 - Prob. 51PPSCh. 3.1 - Prob. 52PPSCh. 3.1 - Prob. 53PPSCh. 3.1 - Prob. 54PPSCh. 3.1 - Prob. 55PPSCh. 3.1 - Prob. 56PPSCh. 3.1 - Prob. 57PPSCh. 3.1 - Prob. 58PPSCh. 3.1 - Prob. 59PPSCh. 3.1 - Prob. 60PPSCh. 3.1 - Prob. 61PPSCh. 3.1 - Prob. 62PPSCh. 3.1 - Prob. 63PPSCh. 3.1 - Prob. 64PPSCh. 3.1 - Prob. 65PPSCh. 3.1 - Prob. 66PPSCh. 3.1 - Prob. 67PPSCh. 3.1 - Prob. 68PPSCh. 3.1 - Prob. 69PPSCh. 3.1 - Prob. 70PPSCh. 3.1 - Prob. 71PPSCh. 3.1 - Prob. 72PPSCh. 3.1 - Prob. 73PPSCh. 3.1 - Prob. 74PPSCh. 3.1 - Prob. 75PPSCh. 3.1 - Prob. 76HPCh. 3.1 - Prob. 77HPCh. 3.1 - Prob. 78HPCh. 3.1 - Prob. 79HPCh. 3.1 - Prob. 80HPCh. 3.1 - Prob. 81STPCh. 3.1 - Prob. 82STPCh. 3.1 - Prob. 83STPCh. 3.1 - Prob. 84STPCh. 3.1 - Prob. 85SRCh. 3.1 - Prob. 86SRCh. 3.1 - Prob. 87SRCh. 3.1 - Prob. 88SRCh. 3.1 - Prob. 89SRCh. 3.1 - Prob. 90SRCh. 3.1 - Prob. 91SRCh. 3.1 - Prob. 92SRCh. 3.1 - Prob. 93SRCh. 3.1 - Prob. 94SRCh. 3.1 - Prob. 95SCh. 3.1 - Prob. 96SCh. 3.1 - Prob. 97SCh. 3.2 - Prob. 1AGPCh. 3.2 - Prob. 1BGPCh. 3.2 - Prob. 2AGPCh. 3.2 - Prob. 2BGPCh. 3.2 - Prob. 3GPCh. 3.2 - Prob. 4AGPCh. 3.2 - Prob. 4BGPCh. 3.2 - Prob. 1CYUCh. 3.2 - Prob. 2CYUCh. 3.2 - Prob. 3CYUCh. 3.2 - Prob. 4CYUCh. 3.2 - Prob. 5CYUCh. 3.2 - Prob. 6CYUCh. 3.2 - Prob. 7PPSCh. 3.2 - Prob. 8PPSCh. 3.2 - Prob. 9PPSCh. 3.2 - Prob. 10PPSCh. 3.2 - Prob. 11PPSCh. 3.2 - Prob. 12PPSCh. 3.2 - Prob. 13PPSCh. 3.2 - Prob. 14PPSCh. 3.2 - Prob. 15PPSCh. 3.2 - Prob. 16PPSCh. 3.2 - Prob. 17PPSCh. 3.2 - Prob. 18PPSCh. 3.2 - Prob. 19PPSCh. 3.2 - Prob. 20PPSCh. 3.2 - Prob. 21PPSCh. 3.2 - Prob. 22PPSCh. 3.2 - Prob. 23PPSCh. 3.2 - Prob. 24PPSCh. 3.2 - Prob. 25PPSCh. 3.2 - Prob. 26PPSCh. 3.2 - Prob. 27PPSCh. 3.2 - Prob. 28PPSCh. 3.2 - Prob. 29PPSCh. 3.2 - Prob. 30PPSCh. 3.2 - Prob. 31PPSCh. 3.2 - Prob. 32PPSCh. 3.2 - Prob. 33PPSCh. 3.2 - Prob. 34PPSCh. 3.2 - Prob. 35PPSCh. 3.2 - Prob. 36PPSCh. 3.2 - Prob. 37PPSCh. 3.2 - Prob. 38PPSCh. 3.2 - Prob. 39PPSCh. 3.2 - Prob. 40PPSCh. 3.2 - Prob. 41PPSCh. 3.2 - Prob. 42PPSCh. 3.2 - Prob. 43PPSCh. 3.2 - Prob. 44PPSCh. 3.2 - Prob. 45HPCh. 3.2 - Prob. 46HPCh. 3.2 - Prob. 47HPCh. 3.2 - Prob. 48HPCh. 3.2 - Prob. 49HPCh. 3.2 - Prob. 50HPCh. 3.2 - Prob. 51STPCh. 3.2 - Prob. 52STPCh. 3.2 - Prob. 53STPCh. 3.2 - Prob. 54STPCh. 3.2 - Prob. 55SRCh. 3.2 - Prob. 56SRCh. 3.2 - Prob. 57SRCh. 3.2 - Prob. 58SRCh. 3.2 - Prob. 59SRCh. 3.2 - Prob. 60SRCh. 3.2 - Prob. 61SRCh. 3.2 - Prob. 62SRCh. 3.2 - Prob. 63SCh. 3.2 - Prob. 64SCh. 3.2 - Prob. 65SCh. 3.2 - Prob. 66SCh. 3.2 - Prob. 67SCh. 3.2 - Prob. 68SCh. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 1AGPCh. 3.3 - Prob. 1BGPCh. 3.3 - Prob. 2AGPCh. 3.3 - Prob. 2BGPCh. 3.3 - Prob. 3GPCh. 3.3 - Prob. 1CYUCh. 3.3 - Prob. 2CYUCh. 3.3 - Prob. 3CYUCh. 3.3 - Prob. 4CYUCh. 3.3 - Prob. 5CYUCh. 3.3 - Prob. 6CYUCh. 3.3 - Prob. 7CYUCh. 3.3 - Prob. 8PPSCh. 3.3 - Prob. 9PPSCh. 3.3 - Prob. 10PPSCh. 3.3 - Prob. 11PPSCh. 3.3 - Prob. 12PPSCh. 3.3 - Prob. 13PPSCh. 3.3 - Prob. 14PPSCh. 3.3 - Prob. 15PPSCh. 3.3 - Prob. 16PPSCh. 3.3 - Prob. 17PPSCh. 3.3 - Prob. 18PPSCh. 3.3 - Prob. 19PPSCh. 3.3 - Prob. 20PPSCh. 3.3 - Prob. 21PPSCh. 3.3 - Prob. 22PPSCh. 3.3 - Prob. 23PPSCh. 3.3 - Prob. 24PPSCh. 3.3 - Prob. 25PPSCh. 3.3 - Prob. 26PPSCh. 3.3 - Prob. 27PPSCh. 3.3 - Prob. 28PPSCh. 3.3 - Prob. 29HPCh. 3.3 - Prob. 30HPCh. 3.3 - Prob. 31HPCh. 3.3 - Prob. 32HPCh. 3.3 - Prob. 33HPCh. 3.3 - Prob. 34STPCh. 3.3 - Prob. 35STPCh. 3.3 - Prob. 36STPCh. 3.3 - Prob. 37STPCh. 3.3 - Prob. 38SRCh. 3.3 - Prob. 39SRCh. 3.3 - Prob. 40SRCh. 3.3 - Prob. 41SRCh. 3.3 - Prob. 42SRCh. 3.3 - Prob. 43SRCh. 3.3 - Prob. 44SRCh. 3.3 - Prob. 45SRCh. 3.3 - Prob. 46SRCh. 3.3 - Prob. 47SRCh. 3.3 - Prob. 48SRCh. 3.3 - Prob. 49SRCh. 3.3 - Prob. 50SCh. 3.3 - Prob. 51SCh. 3.3 - Prob. 52SCh. 3.3 - Prob. 53SCh. 3.3 - Prob. 54SCh. 3.3 - Prob. 55SCh. 3.4 - Prob. 1AGPCh. 3.4 - Prob. 1BGPCh. 3.4 - Prob. 2AGPCh. 3.4 - Prob. 2BGPCh. 3.4 - Prob. 3GPCh. 3.4 - Prob. 1CYUCh. 3.4 - Prob. 2CYUCh. 3.4 - Prob. 3CYUCh. 3.4 - Prob. 4CYUCh. 3.4 - Prob. 5CYUCh. 3.4 - Prob. 6CYUCh. 3.4 - Prob. 7CYUCh. 3.4 - Prob. 8PPSCh. 3.4 - Prob. 9PPSCh. 3.4 - Prob. 10PPSCh. 3.4 - Prob. 11PPSCh. 3.4 - Prob. 12PPSCh. 3.4 - Prob. 13PPSCh. 3.4 - Prob. 14PPSCh. 3.4 - Prob. 15PPSCh. 3.4 - Prob. 16PPSCh. 3.4 - Prob. 17PPSCh. 3.4 - Prob. 18PPSCh. 3.4 - Prob. 19PPSCh. 3.4 - Prob. 20PPSCh. 3.4 - Prob. 21PPSCh. 3.4 - Prob. 22PPSCh. 3.4 - Prob. 23PPSCh. 3.4 - Prob. 24HPCh. 3.4 - Prob. 25HPCh. 3.4 - Prob. 26HPCh. 3.4 - Prob. 27HPCh. 3.4 - Prob. 28HPCh. 3.4 - Prob. 29HPCh. 3.4 - Prob. 30STPCh. 3.4 - Prob. 31STPCh. 3.4 - Prob. 32STPCh. 3.4 - Prob. 33STPCh. 3.4 - Prob. 34SRCh. 3.4 - Prob. 35SRCh. 3.4 - Prob. 36SRCh. 3.4 - Prob. 37SRCh. 3.4 - Prob. 38SRCh. 3.4 - Prob. 39SCh. 3.4 - Prob. 40SCh. 3.4 - Prob. 41SCh. 3.4 - Prob. 42SCh. 3.4 - Prob. 1ECh. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Prob. 12ECh. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - Prob. 16ECh. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.5 - Prob. 1ECh. 3.5 - Prob. 2ECh. 3.5 - Prob. 3ECh. 3.5 - Prob. 4ECh. 3.5 - Prob. 1GPCh. 3.5 - Prob. 2AGPCh. 3.5 - Prob. 2BGPCh. 3.5 - Prob. 2CGPCh. 3.5 - Prob. 3GPCh. 3.5 - Prob. 4GPCh. 3.5 - Prob. 5GPCh. 3.5 - Prob. 1CYUCh. 3.5 - Prob. 2CYUCh. 3.5 - Prob. 3CYUCh. 3.5 - Prob. 4CYUCh. 3.5 - Prob. 5CYUCh. 3.5 - Prob. 6CYUCh. 3.5 - Prob. 7CYUCh. 3.5 - Prob. 8CYUCh. 3.5 - Prob. 9CYUCh. 3.5 - Prob. 10CYUCh. 3.5 - Prob. 11CYUCh. 3.5 - Prob. 12CYUCh. 3.5 - Prob. 13PPSCh. 3.5 - Prob. 14PPSCh. 3.5 - Prob. 15PPSCh. 3.5 - Prob. 16PPSCh. 3.5 - Prob. 17PPSCh. 3.5 - Prob. 18PPSCh. 3.5 - Prob. 19PPSCh. 3.5 - Prob. 20PPSCh. 3.5 - Prob. 21PPSCh. 3.5 - Prob. 22PPSCh. 3.5 - Prob. 23PPSCh. 3.5 - Prob. 24PPSCh. 3.5 - Prob. 25PPSCh. 3.5 - Prob. 26PPSCh. 3.5 - Prob. 27PPSCh. 3.5 - Prob. 28PPSCh. 3.5 - Prob. 29PPSCh. 3.5 - Prob. 30PPSCh. 3.5 - Prob. 31HPCh. 3.5 - Prob. 32HPCh. 3.5 - Prob. 33HPCh. 3.5 - Prob. 34HPCh. 3.5 - Prob. 35HPCh. 3.5 - Prob. 36HPCh. 3.5 - Prob. 37STPCh. 3.5 - Prob. 38STPCh. 3.5 - Prob. 39STPCh. 3.5 - Prob. 40STPCh. 3.5 - Prob. 41SRCh. 3.5 - Prob. 42SRCh. 3.5 - Prob. 43SRCh. 3.5 - Prob. 44SRCh. 3.5 - Prob. 45SRCh. 3.5 - Prob. 46SRCh. 3.5 - Prob. 47SRCh. 3.5 - Prob. 48SRCh. 3.5 - Prob. 49SRCh. 3.5 - Prob. 50SCh. 3.5 - Prob. 51SCh. 3.5 - Prob. 52SCh. 3.6 - Prob. 1AGPCh. 3.6 - Prob. 1BGPCh. 3.6 - Prob. 2GPCh. 3.6 - Prob. 3GPCh. 3.6 - Prob. 4GPCh. 3.6 - Prob. 5GPCh. 3.6 - Prob. 1CYUCh. 3.6 - Prob. 2CYUCh. 3.6 - Prob. 3CYUCh. 3.6 - Prob. 4CYUCh. 3.6 - Prob. 5CYUCh. 3.6 - Prob. 6CYUCh. 3.6 - Prob. 7CYUCh. 3.6 - Prob. 8CYUCh. 3.6 - Prob. 9CYUCh. 3.6 - Prob. 10CYUCh. 3.6 - Prob. 11CYUCh. 3.6 - Prob. 12CYUCh. 3.6 - Prob. 13CYUCh. 3.6 - Prob. 14CYUCh. 3.6 - Prob. 15PPSCh. 3.6 - Prob. 16PPSCh. 3.6 - Prob. 17PPSCh. 3.6 - Prob. 18PPSCh. 3.6 - Prob. 19PPSCh. 3.6 - Prob. 20PPSCh. 3.6 - Prob. 21PPSCh. 3.6 - Prob. 22PPSCh. 3.6 - Prob. 23PPSCh. 3.6 - Prob. 24PPSCh. 3.6 - Prob. 25PPSCh. 3.6 - Prob. 26PPSCh. 3.6 - Prob. 27PPSCh. 3.6 - Prob. 28PPSCh. 3.6 - Prob. 29PPSCh. 3.6 - Prob. 30PPSCh. 3.6 - Prob. 31PPSCh. 3.6 - Prob. 32PPSCh. 3.6 - Prob. 33PPSCh. 3.6 - Prob. 34PPSCh. 3.6 - Prob. 35PPSCh. 3.6 - Prob. 36PPSCh. 3.6 - Prob. 37PPSCh. 3.6 - Prob. 38PPSCh. 3.6 - Prob. 39PPSCh. 3.6 - Prob. 40PPSCh. 3.6 - Prob. 41PPSCh. 3.6 - Prob. 42PPSCh. 3.6 - Prob. 43PPSCh. 3.6 - Prob. 44PPSCh. 3.6 - Prob. 45PPSCh. 3.6 - Prob. 46HPCh. 3.6 - Prob. 47HPCh. 3.6 - Prob. 48HPCh. 3.6 - Prob. 49HPCh. 3.6 - Prob. 50HPCh. 3.6 - Prob. 51STPCh. 3.6 - Prob. 52STPCh. 3.6 - Prob. 53STPCh. 3.6 - Prob. 54STPCh. 3.6 - Prob. 55SRCh. 3.6 - Prob. 56SRCh. 3.6 - Prob. 57SRCh. 3.6 - Prob. 58SRCh. 3.6 - Prob. 59SRCh. 3.6 - Prob. 60SRCh. 3.6 - Prob. 61SRCh. 3.6 - Prob. 62SRCh. 3.6 - Prob. 63SCh. 3.6 - Prob. 64SCh. 3.6 - Prob. 65SCh. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Prob. 8ECh. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.7 - Prob. 1AGPCh. 3.7 - Prob. 1BGPCh. 3.7 - Prob. 2AGPCh. 3.7 - Prob. 2BGPCh. 3.7 - Prob. 3GPCh. 3.7 - Prob. 4AGPCh. 3.7 - Prob. 4BGPCh. 3.7 - Prob. 5AGPCh. 3.7 - Prob. 5BGPCh. 3.7 - Prob. 1CYUCh. 3.7 - Prob. 2CYUCh. 3.7 - Prob. 3CYUCh. 3.7 - Prob. 4CYUCh. 3.7 - Prob. 5CYUCh. 3.7 - Prob. 6CYUCh. 3.7 - Prob. 7CYUCh. 3.7 - Prob. 8CYUCh. 3.7 - Prob. 9CYUCh. 3.7 - Prob. 10CYUCh. 3.7 - Prob. 11CYUCh. 3.7 - Prob. 12CYUCh. 3.7 - Prob. 13CYUCh. 3.7 - Prob. 14CYUCh. 3.7 - Prob. 15CYUCh. 3.7 - Prob. 16CYUCh. 3.7 - Prob. 17CYUCh. 3.7 - Prob. 18CYUCh. 3.7 - Prob. 19CYUCh. 3.7 - Prob. 20CYUCh. 3.7 - Prob. 21CYUCh. 3.7 - Prob. 22CYUCh. 3.7 - Prob. 23CYUCh. 3.7 - Prob. 24CYUCh. 3.7 - Prob. 25CYUCh. 3.7 - Prob. 26PPSCh. 3.7 - Prob. 27PPSCh. 3.7 - Prob. 28PPSCh. 3.7 - Prob. 29PPSCh. 3.7 - Prob. 30PPSCh. 3.7 - Prob. 31PPSCh. 3.7 - Prob. 32PPSCh. 3.7 - Prob. 33PPSCh. 3.7 - Prob. 34PPSCh. 3.7 - Prob. 35PPSCh. 3.7 - Prob. 36PPSCh. 3.7 - Prob. 37PPSCh. 3.7 - Prob. 38PPSCh. 3.7 - Prob. 39PPSCh. 3.7 - Prob. 40PPSCh. 3.7 - Prob. 41PPSCh. 3.7 - Prob. 42PPSCh. 3.7 - Prob. 43PPSCh. 3.7 - Prob. 44PPSCh. 3.7 - Prob. 45PPSCh. 3.7 - Prob. 46PPSCh. 3.7 - Prob. 47PPSCh. 3.7 - Prob. 48PPSCh. 3.7 - Prob. 49PPSCh. 3.7 - Prob. 50PPSCh. 3.7 - Prob. 51PPSCh. 3.7 - Prob. 52PPSCh. 3.7 - Prob. 53PPSCh. 3.7 - Prob. 54PPSCh. 3.7 - Prob. 55PPSCh. 3.7 - Prob. 56HPCh. 3.7 - Prob. 57HPCh. 3.7 - Prob. 58HPCh. 3.7 - Prob. 59HPCh. 3.7 - Prob. 60HPCh. 3.7 - Prob. 61HPCh. 3.7 - Prob. 62STPCh. 3.7 - Prob. 63STPCh. 3.7 - Prob. 64STPCh. 3.7 - Prob. 65STPCh. 3.7 - Prob. 66SRCh. 3.7 - Prob. 67SRCh. 3.7 - Prob. 68SRCh. 3.7 - Prob. 69SRCh. 3.7 - Prob. 70SRCh. 3.7 - Prob. 71SRCh. 3.7 - Prob. 72SRCh. 3.7 - Prob. 73SCh. 3.7 - Prob. 74SCh. 3.7 - Prob. 75SCh. 3.8 - Prob. 1GPCh. 3.8 - Prob. 2AGPCh. 3.8 - Prob. 2BGPCh. 3.8 - Prob. 3GPCh. 3.8 - Prob. 1CYUCh. 3.8 - Prob. 2CYUCh. 3.8 - Prob. 3CYUCh. 3.8 - Prob. 4CYUCh. 3.8 - Prob. 5CYUCh. 3.8 - Prob. 6CYUCh. 3.8 - Prob. 7CYUCh. 3.8 - Prob. 8CYUCh. 3.8 - Prob. 9CYUCh. 3.8 - Prob. 10CYUCh. 3.8 - Prob. 11CYUCh. 3.8 - Prob. 12CYUCh. 3.8 - Prob. 13PPSCh. 3.8 - Prob. 14PPSCh. 3.8 - Prob. 15PPSCh. 3.8 - Prob. 16PPSCh. 3.8 - Prob. 17PPSCh. 3.8 - Prob. 18PPSCh. 3.8 - Prob. 19PPSCh. 3.8 - Prob. 20PPSCh. 3.8 - Prob. 21PPSCh. 3.8 - Prob. 22PPSCh. 3.8 - Prob. 23PPSCh. 3.8 - Prob. 24PPSCh. 3.8 - Prob. 25PPSCh. 3.8 - Prob. 26PPSCh. 3.8 - Prob. 27PPSCh. 3.8 - Prob. 28PPSCh. 3.8 - Prob. 29PPSCh. 3.8 - Prob. 30PPSCh. 3.8 - Prob. 31PPSCh. 3.8 - Prob. 32PPSCh. 3.8 - Prob. 33PPSCh. 3.8 - Prob. 34PPSCh. 3.8 - Prob. 35PPSCh. 3.8 - Prob. 36PPSCh. 3.8 - Prob. 37PPSCh. 3.8 - Prob. 38HPCh. 3.8 - Prob. 39HPCh. 3.8 - Prob. 40HPCh. 3.8 - Prob. 41HPCh. 3.8 - Prob. 42HPCh. 3.8 - Prob. 43STPCh. 3.8 - Prob. 44STPCh. 3.8 - Prob. 45STPCh. 3.8 - Prob. 46STPCh. 3.8 - Prob. 47SRCh. 3.8 - Prob. 48SRCh. 3.8 - Prob. 49SRCh. 3.8 - Prob. 50SRCh. 3.8 - Prob. 51SRCh. 3.8 - Prob. 52SRCh. 3.8 - Prob. 53SRCh. 3.8 - Prob. 54SCh. 3.8 - Prob. 55SCh. 3.8 - Prob. 56SCh. 3.8 - Prob. 1ECh. 3.8 - Prob. 2ECh. 3.8 - Prob. 3ECh. 3.8 - Prob. 4ECh. 3.8 - Prob. 5ECh. 3.8 - Prob. 6ECh. 3 - Prob. 1QCCh. 3 - Prob. 2QCCh. 3 - Prob. 3QCCh. 3 - Prob. 4QCCh. 3 - Prob. 5QCCh. 3 - Prob. 6QCCh. 3 - Prob. 7QCCh. 3 - Prob. 8QCCh. 3 - Prob. 9QCCh. 3 - Prob. 10QCCh. 3 - Prob. 11QCCh. 3 - Prob. 12QCCh. 3 - Prob. 13QCCh. 3 - Prob. 14QCCh. 3 - Prob. 1SGRCh. 3 - Prob. 2SGRCh. 3 - Prob. 3SGRCh. 3 - Prob. 4SGRCh. 3 - Prob. 5SGRCh. 3 - Prob. 6SGRCh. 3 - Prob. 7SGRCh. 3 - Prob. 8SGRCh. 3 - Prob. 9SGRCh. 3 - Prob. 10SGRCh. 3 - Prob. 11SGRCh. 3 - Prob. 12SGRCh. 3 - Prob. 13SGRCh. 3 - Prob. 14SGRCh. 3 - Prob. 15SGRCh. 3 - Prob. 16SGRCh. 3 - Prob. 17SGRCh. 3 - Prob. 18SGRCh. 3 - Prob. 19SGRCh. 3 - Prob. 20SGRCh. 3 - Prob. 21SGRCh. 3 - Prob. 22SGRCh. 3 - Prob. 23SGRCh. 3 - Prob. 24SGRCh. 3 - Prob. 25SGRCh. 3 - Prob. 26SGRCh. 3 - Prob. 27SGRCh. 3 - Prob. 28SGRCh. 3 - Prob. 29SGRCh. 3 - Prob. 30SGRCh. 3 - Prob. 31SGRCh. 3 - Prob. 32SGRCh. 3 - Prob. 33SGRCh. 3 - Prob. 34SGRCh. 3 - Prob. 35SGRCh. 3 - Prob. 36SGRCh. 3 - Prob. 37SGRCh. 3 - Prob. 38SGRCh. 3 - Prob. 39SGRCh. 3 - Prob. 40SGRCh. 3 - Prob. 41SGRCh. 3 - Prob. 42SGRCh. 3 - Prob. 43SGRCh. 3 - Prob. 44SGRCh. 3 - Prob. 45SGRCh. 3 - Prob. 46SGRCh. 3 - Prob. 47SGRCh. 3 - Prob. 48SGRCh. 3 - Prob. 1PTCh. 3 - Prob. 2PTCh. 3 - Prob. 3PTCh. 3 - Prob. 4PTCh. 3 - Prob. 5PTCh. 3 - Prob. 6PTCh. 3 - Prob. 7PTCh. 3 - Prob. 8PTCh. 3 - Prob. 9PTCh. 3 - Prob. 10PTCh. 3 - Prob. 11PTCh. 3 - Prob. 12PTCh. 3 - Prob. 13PTCh. 3 - Prob. 14PTCh. 3 - Prob. 15PTCh. 3 - Prob. 16PTCh. 3 - Prob. 17PTCh. 3 - Prob. 18PTCh. 3 - Prob. 19PTCh. 3 - Prob. 20PTCh. 3 - Prob. 21PTCh. 3 - Prob. 22PTCh. 3 - Prob. 1ECh. 3 - Prob. 2ECh. 3 - Prob. 3ECh. 3 - Prob. 4ECh. 3 - Prob. 5ECh. 3 - Prob. 6ECh. 3 - Prob. 7ECh. 3 - Prob. 8ECh. 3 - Prob. 1STPCh. 3 - Prob. 2STPCh. 3 - Prob. 3STPCh. 3 - Prob. 4STPCh. 3 - Prob. 5STPCh. 3 - Prob. 6STPCh. 3 - Prob. 7STPCh. 3 - Prob. 8STPCh. 3 - Prob. 9STPCh. 3 - Prob. 10STPCh. 3 - Prob. 11STPCh. 3 - Prob. 12STPCh. 3 - Prob. 13STP

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