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Systems of Equations and Inequalities
Barnett, Ziegler, and Byleen, chapter 6
Accurate reckoning--the entrance into the knowledge of
all existing things and all obscure secrets.
Ahmes the Scribe, 17th century B.C.
sections:
6-1, 6-2
Both chapters 6 and 7 are concerned with one topic--the efficient solution of a set of simultaneous
linear equations. We will focus on those systems that have a unique solution; in particular those
with n equations in n unknowns.
objectives:
- tell what is meant by a system of simultaneous linear equations
- distinguish between a system of linear equations and non-linear equations
- translate a real problem into an appropriate system of equations
- explain why a system of equations is preferred to a single equation
- solve a system of two equations by graphing
- solve a system of two equations by substitution
- solve a system of n equations by addition
- describe the possible solutions to a linear system
- show graphically the possible solutions to two equations
- write out the elementary equation operations to produce equivalent systems
- use the elementary equation operations to solve a system
- write out the matrix of coefficients for a system of equations
- produce the augmented matrix
- write out the elementary row operation to produce a equivalent matrix
- identify the transformed matrix that gives the solution
- use the elementary row operations to solve a matrix
- solve a system of equations by the Gauss-Jordan Elimination
- during the solution process, identify when a system does not have a unique solution
Matrices and Determinants
Barnett, Ziegler, and Byleen, chapter 7
sections:
7-1, 7-2, 7-4, 7-5, 7-6
objectives:
- describe what is meant by the dimension of a matrix
- determine the dimension of a matrix
- describe what is meant by the equality of two matrices
- tell when two matrices may be added or subtracted
- add and subtract two compatible matrices
- multiply a matrix by a number
- tell when two matrices may be multiplied
- define a dot product for two matrices
- define a matrix product for two matrices
- identify when two matrices may be multiplied and the dimension of the result
- multiply two matrices together
- write out the properties of matrix multiplication
- transform a system of linear equations into a matrix equation
- describe what is meant by a determinant
- write out the value for a second-order determinant
- define a minor and a cofactor
- evaluate a third-order determinant
- expand an n-th order determinant
- write out the properties of determinants
- use the properties to simplify and evaluate a determinant
- use Cramer's rule to solve a system of simultaneous equations
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© 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 by Lawrence Turner |