PreCalc Chapter 8

Ch 8 Systems of Equations and Inequalities

Ch 8.1 Systems of Equations

Steps of Solving a System of Linear Equations using Substitution Method ;
Solving  and using Substitution Method ;
Solving  and  using Substitution Method ;
Solving  and  using Graphing Calculator ;
Solving  and  using Substitution Method ;
Solving  and  using Substitution Method
https://www.youtube.com/watch?v=HxhacvH49o8

Solving the Following Systems of Equations Using the Substitution Method and Graphing Method  and  ;
and
http://www.youtube.com/watch?v=_teT7HKc0mQ&list=PL554F9F460401DF50&index=34&feature=plpp_video (Part 1 and 2 of the Video)

Ch 8.2 Systems of Linear Equations in Two Variables

Solving  and  using Method of Elimination ;
Steps of Solving a Systems of Linear Equations using Method of Elimination ;
Solving  and  using Method of Elimination ;
Solving  and  using Method of Elimination ;
Finding the Numbers of Minutes for Two Phone Plans which Cost the same
http://www.youtube.com/watch?v=ova8GSmPV4o

Solving  and  using Method of Elimination ;
Solving  and  using Method of Elimination ;
Solving  and  using Method of Elimination ;
Three Possible Solutions : Exactly One Solution, An Infinite Number of Solutions, No solution
http://www.youtube.com/watch?v=_teT7HKc0mQ&list=PL554F9F460401DF50&index=34&feature=plpp_video (Part 3, 4, and 5 Video)

Solving  and  using Method of Elimination
http://www.youtube.com/watch?v=Ywal_dYFuS8&feature=plcp

Solving  and   using Method of Elimination with Infinite Solutions
http://www.youtube.com/watch?v=NRxh9Q16Ulk

Solving  and  using Method of Elimination with No Solutions
http://www.youtube.com/watch?v=z5_ACYtzW98

Finding the Intersection of Two Curves using the TI-83/84 Calculator

http://www.youtube.com/watch?v=amnabT1HLsE&feature=plcp

Ch 8.3 Systems of Inequalities

Finding Solutions and Graphing  ;
Solving Linear Inequality ;
Graphing the System  ,  ,  ,  ;
Graphing the System  ,
http://www.youtube.com/watch?v=IwPBIoz3OWg&list=PL554F9F460401DF50&index=33&feature=plpp_video

Steps of Graphing a Linear Inequality ;
Graphing Inequality  ;
Writing an Inequality to Describe the Graphs ;
Word Problem : Writing an Inequality to Represent the Total Cost of the Seeds, Graphing the Inequality, and Using the Graph to Answer the Questions
http://www.youtube.com/watch?v=RK5bEUDEkaI&list=PLEF97494DFE60E572&index=3&feature=plpp_video

Graphing Inequality  ;
Writing an Inequality to Describe the Graph of Inequality ;
Word Problem : Graphing the Inequality that Represents the Relationship of Two Numbers
http://www.youtube.com/watch?v=tDQD06JZjwY&list=PLEF97494DFE60E572&index=4&feature=plpp_video

Graphing and Solving the Inequalities of  and  ;
Graphing and Solving the Inequalities of  and  ;
Graphing and Solving the Inequalities of  and
http://www.youtube.com/watch?v=ZsmAF10e9Vo

Graphing and Solving the Inequalities of  and
http://www.youtube.com/watch?v=ACTxJv1h2_c

Graphing and Solving the Inequalities of  and
http://www.youtube.com/watch?v=cclH2h1NurM

Graphing and Solving the Inequalities of  and  ,  , and
http://www.youtube.com/watch?v=Egu5DPSBxdk

Ch 8.4 Linear Programming

Minimizing  Subjecting to the Constraints ,  and
http://www.youtube.com/watch?v=I7brzjFhYEU

Linear Programming on Maximizing Profits for Planting Corns and Oats
http://www.youtube.com/watch?v=M4K6HYLHREQ

Linear Programming on Minimizing Cost for Breeding Two Different Brands of Food for Cattle
http://www.youtube.com/watch?v=2ACJ9ewUC6U

Ch 8.5 Systems of Linear Equations in More than Two Variables

Solving the System of Equations using Elimination

http://www.youtube.com/watch?v=vxBSxluknAA&feature=plcp

Introduction to Augmented Matrices (Row Echelon Form) ;
Writing ,  and  as an Augmented Matrix ;
Solving  and  using Row Echelon Form ;
http://www.youtube.com/watch?v=LsnOlNjWWug

Augmented Matrices: Row Echelon Form
Solving  and  ;
Solving  ,  and
http://www.youtube.com/watch?v=BWBckWPjfpw

Solving a System of Two Equations with Using an Augmented Matrix (Row Echelon Form)
and
http://www.youtube.com/watch?v=V8mb5BFmJO0&feature=youtu.be
and
http://www.youtube.com/watch?v=NgXXKmQHFDg&feature=youtu.be
and
http://www.youtube.com/watch?v=9_wGz6zcZ6s&feature=youtu.be

Solving a System of Three Equations with Using an Augmented Matrix (Row Echelon Form)
,  and
http://www.youtube.com/watch?v=WiVeiVIu_SM&feature=youtu.be
,  and
http://www.youtube.com/watch?v=YPgq9K0R3Xw&feature=youtu.be

,  and
http://www.youtube.com/watch?v=co3Yw246mr4&feature=youtu.be

Introduction to Augmented Matrices (Reduced Row Echelon Form) ;
Solving  and  using Reduced Row Echelon Form ;
Solving ,  and  using Reduced Row Echelon Form
http://www.youtube.com/watch?v=-aAucWVD–M

Solving a System of Two Equations with Using an Augmented Matrix (Reduced Row Echelon Form)
and
http://www.youtube.com/watch?v=UK1tOdC7smw&feature=youtu.be
and
http://www.youtube.com/watch?v=tn-c-6m1YO8&feature=youtu.be
and
http://www.youtube.com/watch?v=g521HuccmJo&feature=youtu.be

Solving a System of Three Equations with Using an Augmented Matrix (Reduced Row Echelon Form)
and  and
http://www.youtube.com/watch?v=f5d5y3sr7aE&feature=youtu.be

Augmented Matrices on the Calculator TI83/84
http://www.youtube.com/watch?v=wBmWsW26U7s

Ch 8.6 The Algebra of Matrices

Definition of Matrix ;
Matrix Addition, Subtraction, and Scalar Multiplication
Identifying the Elements , , ,  in the Matrix     ;
Determining , ,  of Matrices  ,  ,  ;
Determining  of Matrix  ;
Determining ,  of Matrices  ,  ,  ,
http://www.youtube.com/watch?v=iNty4CSFIpU

Adding  ;
Adding  ;
Subtracting
http://www.youtube.com/watch?v=cTKjm5fgqKM&feature=youtu.be

Multiplying  ;
Finding  if
http://www.youtube.com/watch?v=kDCka2iqE1Y&feature=youtu.be

Multiplying  given Matrix  and
http://www.youtube.com/watch?v=l–THwUU73g&feature=youtu.be

Application of Matrix Multiplication: Transformations of  and
http://www.youtube.com/watch?v=iWnhjBl5xOs&feature=youtu.be

Ch 8.7 The Inverse of a Matrix

Showing Matrix  is the Inverse of Matrix  and Matrix  is the Inverse of ;
Finding the Inverse Matrix of  ;
Finding the Inverse Matrix of
http://www.youtube.com/watch?v=KBYvP6YG58g

Finding the Inverse Matrix of
http://www.youtube.com/watch?v=zBSl9-KhX58&feature=youtu.be

 

Finding the Inverse Matrix of
http://www.youtube.com/watch?v=NXCz9dw5Ce0&feature=youtu.be

Finding the Inverse Matrix of
http://www.youtube.com/watch?v=6KEmzBwCBzI&feature=youtu.be

Ch 8.8 Determinants

Definition of Determinant of a Matrix ;
Finding the Determinants of  ;
Finding the Determinants of  ;
Finding Determinants of  using Diagonal Method ;
Finding Determinants of  using Method of Cofactors
http://www.youtube.com/watch?v=OI07C1HsOuc

Finding Determinants of  using Method of Cofactors
http://www.youtube.com/watch?v=umXgFjqPfsk&feature=youtu.be

Finding the Determinants of  using Method of Cofactors
http://www.youtube.com/watch?feature=player_embedded&v=21LWuY8i6Hw

Ch 8.9 Properties of Determinants

Using Cramer’s Rule to Solve the Systems of Equations ;
Solving the System of  and  using Cramer’s Rule ;
Solving the System of ,  and  using Cramer’s Rule
http://www.youtube.com/watch?v=ItxF3IjC_uw

Solving the System of  and  using Cramer’s Rule
http://www.youtube.com/watch?v=Z0i_LTUKHVA&feature=youtu.be

Solving the System of ,  and  using Cramer’s Rule
http://www.youtube.com/watch?v=NhSsdEfJIDo&feature=youtu.be

Application of Determinants: Area of Triangle and Parallelogram on the Coordinate Plane
http://www.youtube.com/watch?v=zWI9QeQf2JI

Ch 8.10 Partial Fractions

Steps of Performing Partial Fraction Decomposition ;
Setting Up Partial Fraction Decomposition of Rational Expressions  ,  and
http://www.youtube.com/watch?v=N1lx9yn3SLI&feature=youtu.be

Finding Partial Fraction Decomposition of Rational Expression
http://www.youtube.com/watch?v=O14kJpRMY08&feature=plcp

Finding Partial Fraction Decomposition of Rational Expression   Containing a Linear Factor
http://www.youtube.com/watch?v=WoVdOcuSI0I&feature=youtu.be

Finding Partial Fraction Decomposition of Rational Expression  Containing a Linear Factor
http://www.youtube.com/watch?v=RFTAVAWHgN0&feature=youtu.be

Finding Partial Fraction Decomposition of Rational Expression  Containing a Repeated Linear Factor
http://www.youtube.com/watch?v=6DdwGw_5dvk&feature=youtu.be

Finding Partial Fraction Decomposition of Rational Expression  Containing a Repeated Linear Factor
http://www.youtube.com/watch?v=kKerMmh85EQ&feature=youtu.be

Finding Partial Fraction Decomposition of Rational Expression  Containing Linear Factor and Irreducible Quadratic Factor
http://www.youtube.com/watch?v=prtx4o1wbaQ&feature=youtu.be

Finding Partial Fraction Decomposition of Rational Expression  Containing a Repeating Irreducible Quadratic Factor
http://www.youtube.com/watch?v=Dupeou-FDnI&feature=youtu.be