Section

Content

Suggested Problems

Section 1.1

 linear equation in n variables
 system of m linear equations in n variables
 solution of system of m linear equations in n variables
 solution set of system of m linear equations in n variables
 parameteric representation of solutions
 consistent and inconsistent systems of linear equations
 three types of solutions sets for systems of linear equations
 solution sets with cardinality one (unique solution)
 solution sets with infinite cardinality (infinitely many solutions)
 solution sets with cardinality zero (no solutions  inconsistent)
 back substitution
 equivalent systems of m linear equations in n variables
 operations that produce equivalent systems
 interchange two equations
 multiply an equation by a nonzero number
 add a multiple of one equation to another equation

Pages 1012
14, 7, 9, 1117, 2730, 3738, 4748, 5354, 6768

Section 1.2

 matrix notation
 coefficient matrix of a system of m linear equations in n variables
 augmented matrix for a system of m linear equations in n variables
 elementary row operations
 interchange two rows
 multiply a row by a nonzero number
 add a multiple of one row to a second row and replace the second row
 row echelon form and reduced row echelon form
 Gaussian elimination with back substituion
 GaussJordan elimination
 homoegeous systems of linear equations

Pages 2224
710, 1114, 1924, 2527, 3132, 3536, 4143

Section 1.3

 polynomial curve fitting
 translating large xvalues
 network analysis
 electric circuit analysis

Pages 3234
3, 5, 7, 18, 2728, 31, 33

Section 2.1

 definition of equality for two matrices
 definition of sum for two matrices
 definition of scalar multiplication for a scalar and a matrix
 definition of matrix product for a row vector and a column vector
 definition of product for two matrics
 matrix equation representation of a system of m linear equations in n variables
 solve a system of linear equations via matrix representation
 definition of a linear combination of column vectors

Pages 4851
34, 78, 11, 15, 17, 2122, 2526, 3138, 4142, 4546, 4950

Section 2.2

 algebraic properties of matrix addition and scalar multiplication
 algebraic properties of matrix multiplication
 differences between algebraic properties of real multiplication and matrix multipication
 noncommutativity of multiplication
 noncancellation of multiplication in equations
 three types of solutions sets for systems of linear equations
 solution sets with cardinality one (unique solution)
 solution sets with infinite cardinality (infinitely many solutions)
 solution sets with cardinality zero (no solutions  inconsistent)
 transpose of a matrix
 algebraic properties of transposes

Pages 5961
1, 3, 5, 7, 9, 11, 23, 25, 3334, 37, 39, 43

Section 2.3

 definition of the inverse of a square matrix
 uniqueness of the inverse of a matrix
 finding the inverse of a matrix by GaussJordan elimination
 algebraic properties of the inverse of a matrix
 solving a system of equations using the inverse of a matrix

Pages 7173
3, 5, 7, 9, 1213, 15, 2324, 3133, 41, 45, 47

Section 2.4

 definiton of an elementary matrix
 multiplication by elementary matrices represents elementary row operations
 type I: interchanges two rows upon multiplication (on the left)
 type II: multiplies a row by a nonzero constant upon multiplication (on the left)
 type III: adds a multiple of one row to a second row and replaces the second row with the sum upon multiplication (on the left)
 multiplication of elementary matrix on the right induces action on the columns
 definition of row equivalance of matrices
 elementary matrices are invertible
 Theorem 2.15 on qquivalent conditions for Nonsingularity (pg 78)
 definition of LU factorization of a matric
 construction of LU factorization via (elementary) row reduction
 solving systems of linear equations via LU factorizations

Pages 8283
18, 912, 1314, 1720, 27, 31, 3536, 41, 43, 45
