齐次线性方程作业代写 Competency List by Section

齐次线性方程作业代写

Competency List by Section

齐次线性方程作业代写 Distinguish linear from nonlinear equations (1)Perform Elementary Row Operations (17)Determine if a linear system is consistent

Chapter 1 齐次线性方程作业代写

Section 1.1


  • Terminology

    • Homogeneous linear equation

    • Linear system

    • Unknowns

    • Solution of a linear system

    • Augmented matrix



  • Distinguish linear from nonlinear equations (1)

  • Perform Elementary Row Operations (17)

  • Determine if a linear system is consistent or inconsistent (19)

齐次线性方程作业代写

Section 1.2


  • Terminology

    • Reduced row echelon form

    • Row echelon form

    • Leading one

    • Leading variable

    • Free variable



  • Solve linear system of equations using Gaussian Elimination (5)

  • Solve linear system of equations using Gauss-Jordan Elimination (9)

Section 1.3  齐次线性方程作业代写


  • Terminology

    • Matrix

    • Linear combination of matrices

    • Matrix Transpose

    • Trace of Matrix



  • Represent matrix product as linear combinations

  • Represent linear systems in matrix form Ax=b

Section 1.4


  • Terminology

    • Identity matrix

    • Determinant of a 2x2 matrix



  • Understand Properties of Matrix Arithmetic

  • Understand Properties of Zero Matrices

  • Calculate the determinant of a 2x2 matrix

  • Calculate the inverse of a 2x2 matrix

 

Section 1.5 齐次线性方程作业代写


  • Terminology

    • Row equivalent

    • Elementary matrix

    • Equivalency Theorem



  • Determine inverse of a matrix using elementary row operations

  • Determine if a matrix is invertible

Section 1.6


  • Terminology

    • Equivalency Theorem



  • Solve linear systems using matrix inversion

Section 1.7


  • Terminology

    • Diagonal matrix

    • Triangular matrix

    • Symmetric matrix



  • Determine powers and inverses of diagonal and triangular matrices

Chapter 2  齐次线性方程作业代写

Section 2.1


  • Terminology

    • Determinant

    • Minor of an entry

    • Cofactor an entry



  • Calculate determinants using cofactor expansion

Section 2.2


  • Calculate determinants using row reduction

Section 2.3


  • Terminology

    • Equivalency Theorem



  • Determine invertability using determinants.

EXAM 1

Chapter 3

Section 3.1 齐次线性方程作业代写


  • Terminology

    • Vector

    • Vector Component

    • Ordered n-tuple

    • N-space



  • Be able to add, subtract and translate vectors and multiply vectors with scalars.

Section 3.2


  • Terminology

    • Norm of a vector

    • Unit vector

    • Dot Product



  • Be able to perform vector operations.

  • Calculate dot product of two vectors

Section 3.3  齐次线性方程作业代写


  • Terminology

    • Orthogonal vectors

    • Point-normal form of the equation of a plane



  • Calculate orthogonal projections of vectors

  • Use vectors to derive equations of lines and planes and solve basic geometric problems

Section 3.4


  • Terminology

    • Parametric equations of lines and planes

    • Vector form of the equation of a plane



  • Dot product Form of a Linear System

  • The relationship between Ax=0 and Ax=b

Section 3.5 (Optional)


  • Terminology

    • Cross Product

    • Orthogonal vectors



  • Understand relationships between dot and cross product of two vectors

  • Calculate determinant form of cross product

  • Understand geometric interpretation of cross product

  • Calculate scalar triple product

 

Chapter 4 齐次线性方程作业代写

Section 4.1


  • Terminology

    • Vector Space Axioms



  • Be able to determine if a set in a vector space.

Section 4.2


  • Terminology

    • Subspace

    • Linear combination of vectors

    • Span of Vectors



  • Be able to determine solution spaces of homogeneous systems.

Section 4.3  齐次线性方程作业代写


  • Terminology

    • Linearly dependent and independent

    • Wronskian of a set of functions

    • Span of Vectors



  • Be able to determine if a set of vectors is linearly (in)dependent

  • Be able to determine if a set of functions are linearly (in)dependent

Section 4.4


  • Terminology

    • Basis of vector spaces

    • Coordinates of a vector relative to a basis



  • Be able to determine if a set of vectors forms a basis

  • Be able to determine coordinate vectors relative to a basis

 

Section 4.5  齐次线性方程作业代写


  • Terminology

    • Dimension of a vector space

    • Fundamental theorems



  • Be able to determine the dimensions of a vector space

Section 4.6


  • Be able to determine the transition matrices for changing basis

Section 4.7


  • Terminology

    • Row and column vectors

    • Null, row and column spaces

    • Particular solution

    • General solution



  • Understand the relationships between the solutions of Ax=b and the null, row, column spaces of A

Section 4.8 齐次线性方程作业代写


  • Terminology

    • Rank of a matrix

    • Nullity of a matrix

    • Equivalent Statements

    • Over and underdetermined systems



  • Understand the relationships between the solutions of a linear system and its dimensions

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