齐次线性方程作业代写 Competency List by Section

Competency List by Section

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)

Section 1.2

• Terminology

• Reduced row echelon form

• Row echelon form

• 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.

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