Chapter 12 Matrices

Get Ready!

• Lesson 1-3 Evaluating Expressions

  Evaluate a d − b c bold italic eh bold italic d minus bold italic b bold italic c  for the given values of the variables.

  1. a = − 2 , b = − 2 , c = 5 , d = 4 eh equals negative 2 comma b equals negative 2 comma c equals 5 comma d equals 4
  2. a = 1 2 , b = − 1 , c = − 2 3 , d = 2 eh equals , 1 half , comma b equals negative 1 comma c equals negative , 2 thirds , comma d equals 2
  3. a = 2 , b = 1 2 , c = 1 4 , d = − 1 8 eh equals 2 comma b equals , 1 half , comma c equals , 1 fourth , comma d equals negative , 1 eighth
  4. a = − 1 3 , b = 1 2 , c = 1 4 , d = − 2 3 eh equals negative , 1 third , comma b equals , 1 half , comma c equals , 1 fourth , comma d equals negative , 2 thirds

• Lesson 3-6 Identifying Matrix Elements

  Identify the indicated element.

  A = [ 2 − 1 3 5 7 − 9 4 11 21 ] eh equals left bracket . table with 3 rows and 3 columns , row1 column 1 , 2 , column 2 negative 1 , column 3 3 , row2 column 1 , 5 , column 2 7 , column 3 negative 9 , row3 column 1 , 4 , column 2 11 , column 3 21 , end table . right bracket

  5. a 23 eh sub 23
  6. a 32 eh sub 32
  7. a 13 eh sub 13

• Lessons 3-2 and 3-6 Solving Systems of Equations

  Solve each system.

  8. { − 2 x + y = − 5 4 x + y = − 2 left brace . table with 2 rows and 1 column , row1 column 1 , negative 2 x plus y equals negative 5 , row2 column 1 , 4 x plus y equals negative 2 , end table
  9. { 4 x − y = − 2 − 1 2 x − y = 1 left brace . table with 2 rows and 2 columns , row1 column 1 , 4 x minus y equals , column 2 negative 2 , row2 column 1 , negative , 1 half , x minus y equals , column 2 1 , end table
  10. { 3 x + y = 5 − x + y = 2 left brace . table with 2 rows and 1 column , row1 column 1 , 3 x plus y equals 5 , row2 column 1 , negative x plus y equals 2 , end table
  11. { x + y + z = 10 2 z − y = 5 y − z = 15 left brace . table with 3 rows and 3 columns , row1 column 1 , x plus y , column 2 plus z equals , column 3 10 , row2 column 1 , 2 z minus y , column 2 equals , column 3 5 , row3 column 1 , y , column 2 negative z equals , column 3 15 , end table
  12. { − x + y + 2 z = 16 2 x − 2 y − 2 z = − 16 x + y = 0 left brace . table with 3 rows and 4 columns , row1 column 1 , negative x plus , column 2 y , column 3 plus 2 z equals , column 4 16 , row2 column 1 , 2 x minus , column 2 2 y , column 3 negative 2 z equals , column 4 negative 16 , row3 column 1 , x plus , column 2 y , column 3 equals , column 4 0 , end table
  13. { − 2 x + 3 y + z = 1 x − 3 z = 7   − y + z = − 5 left brace . table with 3 rows and 4 columns , row1 column 1 , negative 2 x plus , column 2 3 y plus , column 3 z equals , column 4 1 , row2 column 1 , x , column 2 minus , column 3 3 z equals , column 4 7 , row3 column 1 , , column 2 negative y plus , column 3 z equals , column 4 negative 5 , end table

Table of Contents