1. Ed and Diane are on the beach to observe a green flash. As the very last sliver of
the sun sinks into the ocean, refraction bends the final ray of sunlight into a
rainbow of colors. The red and orange set first, and the green light or green flash
is th
Take-Home Test 1
Question:
You work as an inspector for an insurance company. One of your clients has filed a
claim for medical problems sustained from an accident at a carnival in which he fell
out of the seat of a ferris wheel 40 seconds into the ride.
1. Your company must make a triangular part for one of its machines and the only
info they gave you for the part is that two adjacent sides are 35 cm and 50 cm,
and the angle opposite the 35 cm side measures 26 degrees. Your boss says to
write a short rep
Outline
Linear Systems
Matrices
Gaussian Elimination
Solving Linear Systems of Equations
Math 2270
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Homogeneous Systems
Outline
Linear Systems
Matrices
Outline
1
Linear Systems
Linear Eq
Outline
Number of Solutions
Solving Multiple Systems
More Results On the Inverse
Inverses and Linear Systems of Equations
Math 2270
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Outline
Number of Solutions
Solving Multiple Systems
Outline
Identity Matrices
The Inverse of a Matrix
Math 2270
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Inverse of a Matrix
Outline
Identity Matrices
Outline
1
Identity Matrices
2
Inverse of a Matrix
The Inverse of a Matrix
Inver
Outline
Elementary Matrix
Inverse of an Elementary Matrix
Elementary Matrices
Math 2270
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
The Inverse of a Matrix
Outline
Elementary Matrix
Inverse of an Elementary Matrix
Outline
1
Eleme
Outline
Matrices
Matrix Algebra
Matrix Equations
Matrix Algebra
Math 2270
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Trace and Transpose
Outline
Matrices
Matrix Algebra
Matrix Equations
Trace and Transpose
Outline
1
Matrices
2
M
Outline
Diagonal Matrices
Triangular Matrices
Special Matrices
Math 2270
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Symmetric Matrices
Outline
Diagonal Matrices
Outline
1
Diagonal Matrices
2
Triangular Matrices
3
Symmetric Matri
The Determinant of a Matrix
Math 2270
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Outline
The Determinant of a 2 2 Matrix
Denition
If A is the 2 2 matrix
A=
ab
cd
then the determinant of A to is the number det A or |A| dened by:
Outline
Vector Quantities
Combining Vectors
Vectors in the Plane
Geometric Vectors
Math 2270
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Vectors in Space
The Norm
Outline
Vector Quantities
Combining Vectors
Vectors in the Plane
O
Outline
The Classical Adjoint
A Formula for the Inverse of a Matrix
Cramers Rule
Applications of the Determinant
Math 2270
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Eigenvalues
Outline
The Classical Adjoint
A Formula for the In
Outline
Linearity of the Determinant
Determinants and Invertibility
Determinants and Products
Properties of the Determinant
Math 2270
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Determinants and Inverses
Outline
Linearity of the
Outline Determinants of Special Matrices Determinants Via Elementary Row Operations Determinant of an Elementary Matrix
Computing the Determinant Via Row Reduction
Math 2270
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Outline Det
Math 1050 Exam 1 Review Sheet
Exam 1 will cover sections R.1, R.2, R.3, R.4, R.5, R.6, 1.1, 1.2, 1.3, 1.4
Student Learning Outcomes Tested
1. Be procient at simplifying expressions using algebraic properties of real numbers.
2. Be procient at factoring po
Outline
Quadratic Equations
Solving Quadratic Equations
Quadratic Equations
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Applications
Outline
Quadratic Equations
Outline
1
Quadratic Equations
2
Solving Quadratic Equation
Outline
Imaginary Numbers
Complex Numbers
The Arithmetic of the Complex Numbers
The Complex Number System
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Outline
Imaginary Numbers
Complex Numbers
The Arithmetic of the Compl
Outline
Equations Involving Absolute Value
Inequalities Involving Absolute Value
Equations and Inequalities Involving Absolute
Value
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Applications
Outline
Equations Involving A
Outline
Linear Equations
Linear Equations
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Equations in More Than One Variable
Outline
Linear Equations
Equations in More Than One Variable
Outline
1
Linear Equations
Linear Eq
Outline
Inequalities
Properties of Inequalities
Compound Inequalities
Linear Inequalities in One Variable
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Applications
Outline
Inequalities
Properties of Inequalities
Outline
Outline
Solving Polynomial Equations
Solving Rational Equations
Solving Equations
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Rational Exponents
Applications
Outline
Solving Polynomial Equations
Solving Rational Equatio
Outline
Relations
Graphing Relations
Rectangular Coordinates and Relations
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Circles
Outline
Relations
Graphing Relations
Outline
1
Relations
2
Graphing Relations
The Rectangula
Outline
Basic Functions
Translations
Reections
Scaling
Basic Functions and Transformations
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
General Transformations
Outline
Basic Functions
Translations
Outline
1
Basic Functio
Outline
Piecewise-Dened Functions
Graphing Piecewise-Dened Functions
Piecewise-Dened Functions
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Applications
Outline
Piecewise-Dened Functions
Graphing Piecewise-Dened Function
Outline
Symmetry
Positive/Negative
Increasing/Decreasing
Maximum/Minimum
The Graph of a Function
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
The Dierence Quotient
Outline
Symmetry
Positive/Negative
Increasing/Decreasing
Outline
Functions
Representing Functions
The Domain and Range
Evaluating Functions
Functions and Their Graphs
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Average Rate of Change
Outline
Functions
Representing Functions
T
Outline
Linear Equations
Graphing Linear Equations
The Slope of a Line
Graphs of Linear Equations
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Applications
Outline
Linear Equations
Graphing Linear Equations
Outline
1
Lin
Outline
Three Forms of a Linear Equation
Graphing Linear Equations
The Point-Slope Form of a Line
Forms of Linear Equations
Math 1050
K. J. Platt, Ph.D.
Department of Mathematics
Snow College
Spring 2014
Applications
Outline
Three Forms of a Linear Equati
2.1 Linear Equations in
One Variable
By: Cindy Alder
Objectives:
Distinguish between expressions and equations.
Identify linear equations, and decide whether a number is
a solution of a linear equation.
Solve linear equations by using the addition and
2.6 Set Operations &
Compound Inequalities
By: Cindy Alder
Objectives:
Find the intersection of two sets.
Solve compound inequalities with the
word and.
Find the union of two sets.
Solve compound inequalities with the
word or.
Intersection & Union of