High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
15th Edition
ISBN: 9780133281163
Author: Prentice Hall
Publisher: Prentice Hall
Expert Solution & Answer
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Chapter 12.2, Problem 47PPSE
Solution

Whether the two expressions P+QR+S and P+QR+P+QS are equal or not.

Yes, both expressions are equal that is P+QR+S=P+QR+P+QS .

Given information: Matrices are P=3412,Q=1032,R=1421 and S=0121 .

Formula used:

Matrix multiplication is,

  a11a12a21a22b11b12b21b22=a11b11+a12b21a11b12+a12b22a21b11+a22b21a21b12+a22b22 .

Calculation:

Consider the matrices as P=3412,Q=1032,R=1421 and S=0121 .

Now,

  P+QR+S=3412+10321421+0121=3+14+01+32+21+04+12+21+1=44401502=4×1+4×04×5+4×24×1+0×04×5+0×2

Further,

  P+QR+S=4+020+84+020+0=428420

Also,

   P+Q R+ P+Q S= 3 4 1 2 + 1 0 3 2 1 4 2 1 + 3 4 1 2 + 1 0 3 2 0 1 2 1

   = 3+1 4+0 1+3 2+ 2 1 4 2 1 + 3+1 4+0 1+3 2+ 2 0 1 2 1

   = 4 4 4 0 1 4 2 1 + 4 4 4 0 0 1 2 1

   = 4×1+4× 2 4×4+4×1 4×1+0× 2 4×4+0×1 + 4×0+4×2 4×1+4×1 4×0+0×2 4×1+0×1

Further,

  P+QR+P+QS=4816+44+016+0+0+84+40+04+0=420416+8804=4+820+84+016+4=428420

Therefore, P+QR+S=P+QR+P+QS .

Chapter 12 Solutions

High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

Ch. 12.1 - Prob. 11PPSECh. 12.1 - Prob. 12PPSECh. 12.1 - Prob. 13PPSECh. 12.1 - Prob. 14PPSECh. 12.1 - Prob. 15PPSECh. 12.1 - Prob. 16PPSECh. 12.1 - Prob. 17PPSECh. 12.1 - Prob. 18PPSECh. 12.1 - Prob. 19PPSECh. 12.1 - Prob. 20PPSECh. 12.1 - Prob. 21PPSECh. 12.1 - Prob. 22PPSECh. 12.1 - Prob. 23PPSECh. 12.1 - Prob. 24PPSECh. 12.1 - Prob. 25PPSECh. 12.1 - Prob. 26PPSECh. 12.1 - Prob. 27PPSECh. 12.1 - Prob. 28PPSECh. 12.1 - Prob. 29PPSECh. 12.1 - Prob. 30PPSECh. 12.1 - Prob. 31PPSECh. 12.1 - Prob. 32PPSECh. 12.1 - Prob. 33PPSECh. 12.1 - Prob. 34PPSECh. 12.1 - Prob. 35PPSECh. 12.1 - Prob. 36PPSECh. 12.1 - Prob. 37PPSECh. 12.1 - Prob. 38PPSECh. 12.1 - Prob. 39PPSECh. 12.1 - Prob. 40PPSECh. 12.1 - Prob. 41PPSECh. 12.1 - Prob. 42PPSECh. 12.1 - Prob. 43PPSECh. 12.1 - Prob. 44PPSECh. 12.1 - Prob. 45PPSECh. 12.1 - Prob. 1ECh. 12.1 - Prob. 2ECh. 12.1 - Prob. 3ECh. 12.1 - Prob. 4ECh. 12.1 - Prob. 5ECh. 12.1 - Prob. 6ECh. 12.2 - Prob. 1LCCh. 12.2 - Prob. 2LCCh. 12.2 - Prob. 3LCCh. 12.2 - Prob. 4LCCh. 12.2 - Prob. 5LCCh. 12.2 - Prob. 6LCCh. 12.2 - Prob. 7PPSECh. 12.2 - Prob. 8PPSECh. 12.2 - Prob. 9PPSECh. 12.2 - Prob. 10PPSECh. 12.2 - Prob. 11PPSECh. 12.2 - Prob. 12PPSECh. 12.2 - Prob. 13PPSECh. 12.2 - Prob. 14PPSECh. 12.2 - Prob. 15PPSECh. 12.2 - Prob. 16PPSECh. 12.2 - Prob. 17PPSECh. 12.2 - Prob. 18PPSECh. 12.2 - Prob. 19PPSECh. 12.2 - Prob. 20PPSECh. 12.2 - Prob. 21PPSECh. 12.2 - Prob. 22PPSECh. 12.2 - Prob. 23PPSECh. 12.2 - Prob. 24PPSECh. 12.2 - Prob. 25PPSECh. 12.2 - Prob. 26PPSECh. 12.2 - Prob. 27PPSECh. 12.2 - Prob. 28PPSECh. 12.2 - Prob. 29PPSECh. 12.2 - Prob. 30PPSECh. 12.2 - Prob. 31PPSECh. 12.2 - Prob. 32PPSECh. 12.2 - Prob. 33PPSECh. 12.2 - Prob. 34PPSECh. 12.2 - Prob. 35PPSECh. 12.2 - Prob. 36PPSECh. 12.2 - Prob. 37PPSECh. 12.2 - Prob. 38PPSECh. 12.2 - Prob. 39PPSECh. 12.2 - Prob. 40PPSECh. 12.2 - Prob. 41PPSECh. 12.2 - Prob. 42PPSECh. 12.2 - Prob. 43PPSECh. 12.2 - Prob. 44PPSECh. 12.2 - Prob. 45PPSECh. 12.2 - Prob. 46PPSECh. 12.2 - Prob. 47PPSECh. 12.2 - Prob. 48PPSECh. 12.2 - Prob. 1ECh. 12.2 - Prob. 2ECh. 12.2 - Prob. 3ECh. 12.2 - Prob. 4ECh. 12.2 - Prob. 5ECh. 12.2 - Prob. 6ECh. 12.2 - Prob. 7ECh. 12.2 - Prob. 8ECh. 12.2 - Prob. 9ECh. 12.2 - Prob. 10ECh. 12.3 - Prob. 1LCCh. 12.3 - Prob. 2LCCh. 12.3 - Prob. 3LCCh. 12.3 - Prob. 4LCCh. 12.3 - Prob. 5LCCh. 12.3 - Prob. 6LCCh. 12.3 - Prob. 7PPSECh. 12.3 - Prob. 8PPSECh. 12.3 - Prob. 9PPSECh. 12.3 - Prob. 10PPSECh. 12.3 - Prob. 11PPSECh. 12.3 - Prob. 12PPSECh. 12.3 - Prob. 13PPSECh. 12.3 - Prob. 14PPSECh. 12.3 - Prob. 15PPSECh. 12.3 - Prob. 16PPSECh. 12.3 - Prob. 17PPSECh. 12.3 - Prob. 18PPSECh. 12.3 - Prob. 19PPSECh. 12.3 - Prob. 20PPSECh. 12.3 - Prob. 21PPSECh. 12.3 - Prob. 22PPSECh. 12.3 - Prob. 23PPSECh. 12.3 - Prob. 24PPSECh. 12.3 - Prob. 25PPSECh. 12.3 - Prob. 26PPSECh. 12.3 - Prob. 27PPSECh. 12.3 - Prob. 28PPSECh. 12.3 - Prob. 29PPSECh. 12.3 - Prob. 30PPSECh. 12.3 - Prob. 31PPSECh. 12.3 - Prob. 32PPSECh. 12.3 - Prob. 33PPSECh. 12.3 - Prob. 34PPSECh. 12.3 - Prob. 35PPSECh. 12.3 - Prob. 36PPSECh. 12.3 - Prob. 37PPSECh. 12.3 - Prob. 38PPSECh. 12.3 - Prob. 39PPSECh. 12.3 - Prob. 40PPSECh. 12.3 - Prob. 41PPSECh. 12.3 - Prob. 42PPSECh. 12.3 - Prob. 43PPSECh. 12.3 - Prob. 44PPSECh. 12.3 - Prob. 45PPSECh. 12.3 - Prob. 46PPSECh. 12.3 - Prob. 47PPSECh. 12.3 - Prob. 48PPSECh. 12.3 - Prob. 49PPSECh. 12.3 - Prob. 50PPSECh. 12.3 - Prob. 51PPSECh. 12.3 - Prob. 52PPSECh. 12.3 - Prob. 53PPSECh. 12.3 - Prob. 54PPSECh. 12.3 - Prob. 55PPSECh. 12.3 - Prob. 56PPSECh. 12.3 - Prob. 57PPSECh. 12.3 - Prob. 58PPSECh. 12.3 - Prob. 59PPSECh. 12.3 - Prob. 60PPSECh. 12.3 - Prob. 61PPSECh. 12.3 - Prob. 62PPSECh. 12.3 - Prob. 63PPSECh. 12.3 - Prob. 64PPSECh. 12.3 - Prob. 65PPSECh. 12.3 - Prob. 66PPSECh. 12.3 - Prob. 67PPSECh. 12.3 - Prob. 68PPSECh. 12.3 - Prob. 69PPSECh. 12.3 - Prob. 70PPSECh. 12.3 - Prob. 71PPSECh. 12.3 - Prob. 72PPSECh. 12.3 - Prob. 73PPSECh. 12.3 - Prob. 74PPSECh. 12.3 - Prob. 75PPSECh. 12.3 - Prob. 76PPSECh. 12.4 - Prob. 1LCCh. 12.4 - Prob. 2LCCh. 12.4 - Prob. 3LCCh. 12.4 - Prob. 4LCCh. 12.4 - Prob. 5LCCh. 12.4 - Prob. 6LCCh. 12.4 - Prob. 7PPSECh. 12.4 - Prob. 8PPSECh. 12.4 - Prob. 9PPSECh. 12.4 - Prob. 10PPSECh. 12.4 - Prob. 11PPSECh. 12.4 - Prob. 12PPSECh. 12.4 - Prob. 13PPSECh. 12.4 - Prob. 14PPSECh. 12.4 - Prob. 15PPSECh. 12.4 - Prob. 16PPSECh. 12.4 - Prob. 17PPSECh. 12.4 - Prob. 18PPSECh. 12.4 - Prob. 19PPSECh. 12.4 - Prob. 20PPSECh. 12.4 - Prob. 21PPSECh. 12.4 - Prob. 22PPSECh. 12.4 - Prob. 23PPSECh. 12.4 - Prob. 24PPSECh. 12.4 - Prob. 25PPSECh. 12.4 - Prob. 26PPSECh. 12.4 - Prob. 27PPSECh. 12.4 - Prob. 28PPSECh. 12.4 - Prob. 29PPSECh. 12.4 - Prob. 30PPSECh. 12.4 - Prob. 31PPSECh. 12.4 - Prob. 32PPSECh. 12.4 - Prob. 33PPSECh. 12.4 - Prob. 34PPSECh. 12.4 - Prob. 35PPSECh. 12.4 - Prob. 36PPSECh. 12.4 - Prob. 37PPSECh. 12.4 - Prob. 38PPSECh. 12.4 - Prob. 39PPSECh. 12.4 - Prob. 40PPSECh. 12.4 - Prob. 41PPSECh. 12.4 - Prob. 42PPSECh. 12.4 - Prob. 43PPSECh. 12.4 - Prob. 44PPSECh. 12.4 - Prob. 45PPSECh. 12.4 - Prob. 46PPSECh. 12.4 - Prob. 47PPSECh. 12.4 - Prob. 48PPSECh. 12.4 - Prob. 49PPSECh. 12.4 - Prob. 50PPSECh. 12.4 - Prob. 51PPSECh. 12.4 - Prob. 52PPSECh. 12.4 - Prob. 53PPSECh. 12.4 - Prob. 54PPSECh. 12.4 - Prob. 55PPSECh. 12.4 - Prob. 56PPSECh. 12.4 - Prob. 57PPSECh. 12.4 - Prob. 58PPSECh. 12.4 - Prob. 59PPSECh. 12.4 - Prob. 60PPSECh. 12.4 - Prob. 61PPSECh. 12.4 - Prob. 62PPSECh. 12.5 - Prob. 1LCCh. 12.5 - Prob. 2LCCh. 12.5 - Prob. 3LCCh. 12.5 - Prob. 4LCCh. 12.5 - Prob. 5LCCh. 12.5 - Prob. 6LCCh. 12.5 - Prob. 7PPSECh. 12.5 - Prob. 8PPSECh. 12.5 - Prob. 9PPSECh. 12.5 - Prob. 10PPSECh. 12.5 - Prob. 11PPSECh. 12.5 - Prob. 12PPSECh. 12.5 - Prob. 13PPSECh. 12.5 - Prob. 14PPSECh. 12.5 - Prob. 15PPSECh. 12.5 - Prob. 16PPSECh. 12.5 - Prob. 17PPSECh. 12.5 - Prob. 18PPSECh. 12.5 - Prob. 19PPSECh. 12.5 - Prob. 20PPSECh. 12.5 - Prob. 21PPSECh. 12.5 - Prob. 22PPSECh. 12.5 - Prob. 23PPSECh. 12.5 - Prob. 24PPSECh. 12.5 - Prob. 25PPSECh. 12.5 - Prob. 26PPSECh. 12.5 - Prob. 27PPSECh. 12.5 - Prob. 28PPSECh. 12.5 - Prob. 29PPSECh. 12.5 - Prob. 30PPSECh. 12.5 - Prob. 31PPSECh. 12.5 - Prob. 32PPSECh. 12.5 - Prob. 33PPSECh. 12.5 - Prob. 34PPSECh. 12.5 - Prob. 35PPSECh. 12.5 - Prob. 36PPSECh. 12.5 - Prob. 37PPSECh. 12.5 - Prob. 38PPSECh. 12.5 - Prob. 39PPSECh. 12.5 - Prob. 40PPSECh. 12.5 - Prob. 41PPSECh. 12.5 - Prob. 42PPSECh. 12.5 - Prob. 43PPSECh. 12.5 - Prob. 44PPSECh. 12.5 - Prob. 45PPSECh. 12.5 - Prob. 46PPSECh. 12.5 - Prob. 47PPSECh. 12.5 - Prob. 48PPSECh. 12.5 - Prob. 49PPSECh. 12.5 - Prob. 50PPSECh. 12.5 - Prob. 51PPSECh. 12.5 - Prob. 52PPSECh. 12.6 - Prob. 1LCCh. 12.6 - Prob. 2LCCh. 12.6 - Prob. 3LCCh. 12.6 - Prob. 4LCCh. 12.6 - Prob. 5LCCh. 12.6 - Prob. 6LCCh. 12.6 - Prob. 7PPSECh. 12.6 - Prob. 8PPSECh. 12.6 - Prob. 9PPSECh. 12.6 - Prob. 10PPSECh. 12.6 - Prob. 11PPSECh. 12.6 - Prob. 12PPSECh. 12.6 - Prob. 13PPSECh. 12.6 - Prob. 14PPSECh. 12.6 - Prob. 15PPSECh. 12.6 - Prob. 16PPSECh. 12.6 - Prob. 17PPSECh. 12.6 - Prob. 18PPSECh. 12.6 - Prob. 19PPSECh. 12.6 - Prob. 20PPSECh. 12.6 - Prob. 21PPSECh. 12.6 - Prob. 22PPSECh. 12.6 - Prob. 23PPSECh. 12.6 - Prob. 24PPSECh. 12.6 - Prob. 25PPSECh. 12.6 - Prob. 26PPSECh. 12.6 - Prob. 27PPSECh. 12.6 - Prob. 28PPSECh. 12.6 - Prob. 29PPSECh. 12.6 - Prob. 30PPSECh. 12.6 - Prob. 31PPSECh. 12.6 - Prob. 32PPSECh. 12.6 - Prob. 33PPSECh. 12.6 - Prob. 34PPSECh. 12.6 - Prob. 35PPSECh. 12.6 - Prob. 36PPSECh. 12.6 - Prob. 37PPSECh. 12.6 - Prob. 38PPSECh. 12.6 - Prob. 39PPSECh. 12.6 - Prob. 40PPSECh. 12.6 - Prob. 41PPSECh. 12.6 - Prob. 42PPSECh. 12.6 - Prob. 43PPSECh. 12.6 - Prob. 44PPSECh. 12.6 - Prob. 45PPSECh. 12.6 - Prob. 46PPSECh. 12.6 - Prob. 47PPSECh. 12.6 - Prob. 48PPSECh. 12.6 - Prob. 49PPSECh. 12.6 - Prob. 50PPSECh. 12.6 - Prob. 51PPSECh. 12.6 - Prob. 52PPSECh. 12.6 - Prob. 53PPSECh. 12 - Prob. 1GRCh. 12 - Prob. 2GRCh. 12 - Prob. 3GRCh. 12 - Prob. 4GRCh. 12 - Prob. 5GRCh. 12 - Prob. 6GRCh. 12 - Prob. 7GRCh. 12 - Prob. 8GRCh. 12 - Prob. 9GRCh. 12 - Prob. 10GRCh. 12 - Prob. 11GRCh. 12 - Prob. 12GRCh. 12 - Prob. 13GRCh. 12 - Prob. 14GRCh. 12 - Prob. 15GRCh. 12 - Prob. 1MCQCh. 12 - Prob. 2MCQCh. 12 - Prob. 3MCQCh. 12 - Prob. 4MCQCh. 12 - Prob. 5MCQCh. 12 - Prob. 6MCQCh. 12 - Prob. 7MCQCh. 12 - Prob. 8MCQCh. 12 - Prob. 9MCQCh. 12 - Prob. 10MCQCh. 12 - Prob. 11MCQCh. 12 - Prob. 12MCQCh. 12 - Prob. 13MCQCh. 12 - Prob. 14MCQCh. 12 - Prob. 15MCQCh. 12 - Prob. 16MCQCh. 12 - Prob. 17MCQCh. 12 - Prob. 18MCQCh. 12 - Prob. 19MCQCh. 12 - Prob. 20MCQCh. 12 - Prob. 21MCQCh. 12 - Prob. 22MCQCh. 12 - Prob. 23MCQCh. 12 - Prob. 24MCQCh. 12 - Prob. 25MCQCh. 12 - Prob. 26MCQCh. 12 - Prob. 27MCQCh. 12 - Prob. 1CVCh. 12 - Prob. 2CVCh. 12 - Prob. 3CVCh. 12 - Prob. 4CVCh. 12 - Prob. 5ECh. 12 - Prob. 6ECh. 12 - Prob. 7ECh. 12 - Prob. 8ECh. 12 - Prob. 9ECh. 12 - Prob. 10ECh. 12 - Prob. 11ECh. 12 - Prob. 12ECh. 12 - Prob. 13ECh. 12 - Prob. 14ECh. 12 - Prob. 15ECh. 12 - Prob. 16ECh. 12 - Prob. 17ECh. 12 - Prob. 18ECh. 12 - Prob. 19ECh. 12 - Prob. 20ECh. 12 - Prob. 21ECh. 12 - Prob. 22ECh. 12 - Prob. 23ECh. 12 - Prob. 24ECh. 12 - Prob. 25ECh. 12 - Prob. 26ECh. 12 - Prob. 27ECh. 12 - Prob. 28ECh. 12 - Prob. 29ECh. 12 - Prob. 30ECh. 12 - Prob. 31ECh. 12 - Prob. 32ECh. 12 - Prob. 33ECh. 12 - Prob. 34ECh. 12 - Prob. 35ECh. 12 - Prob. 36ECh. 12 - Prob. 37ECh. 12 - Prob. 38ECh. 12 - Prob. 39ECh. 12 - Prob. 40ECh. 12 - Prob. 1CTCh. 12 - Prob. 2CTCh. 12 - Prob. 3CTCh. 12 - Prob. 4CTCh. 12 - Prob. 5CTCh. 12 - Prob. 6CTCh. 12 - Prob. 7CTCh. 12 - Prob. 8CTCh. 12 - Prob. 9CTCh. 12 - Prob. 10CTCh. 12 - Prob. 11CTCh. 12 - Prob. 12CTCh. 12 - Prob. 13CTCh. 12 - Prob. 14CTCh. 12 - Prob. 15CTCh. 12 - Prob. 16CTCh. 12 - Prob. 17CTCh. 12 - Prob. 18CTCh. 12 - Prob. 19CTCh. 12 - Prob. 20CTCh. 12 - Prob. 21CTCh. 12 - Prob. 22CTCh. 12 - Prob. 23CTCh. 12 - Prob. 24CTCh. 12 - Prob. 25CTCh. 12 - Prob. 26CTCh. 12 - Prob. 27CTCh. 12 - Prob. 28CTCh. 12 - Prob. 29CTCh. 12 - Prob. 30CTCh. 12 - Prob. 31CTCh. 12 - Prob. 32CTCh. 12 - Prob. 33CTCh. 12 - Prob. 34CTCh. 12 - Prob. 1CCSRCh. 12 - Prob. 2CCSRCh. 12 - Prob. 3CCSRCh. 12 - Prob. 4CCSRCh. 12 - Prob. 5CCSRCh. 12 - Prob. 6CCSRCh. 12 - Prob. 7CCSRCh. 12 - Prob. 8CCSRCh. 12 - Prob. 9CCSRCh. 12 - Prob. 10CCSRCh. 12 - Prob. 11CCSRCh. 12 - Prob. 12CCSRCh. 12 - 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