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Summary: Review Sheet: Chapter Three
Jingrun Chen
Math 3C, Spring 2011
LINEAR ALGEBRA
· Matrix Terminology & Corresponding Properties: Dimension (Or-
der), Element (Entry), Row Vector, Column Vector, Square Matrix,
Diagonal Element, Augmented Matrix, Reduced Row Echelon Form
(RREF), Inverse Matrix
· Special Matrix & Corresponding Properties: Zero Matrix, Diagonal
Matrix, Identity Matrix
· Operation for Single Matrix & Corresponding Properties: Scalar Mul-
tiplication, Determinant, Elementary Row (Column) Operations,
· Matrix Arithmetic (Between Matrices) & Corresponding Properties:
Addition, Subtraction, Multiplication, Division
· Be Able to Solve Systems of Linear (Algebraic) Equations by Gaus-
sian Elimination for Different Cases: Unique Solution, Infinitely Many
Solutions, No Solution; Understand Correspondence Between Pivot,
Rank, Invertibility, Singularity & Number of Solutions; Be Able to
Solve Linear Systems by Nonhomogeneous Principle & Cramer's Rule
· Vector Space (Ten Conditions), Subspace (Two Conditions) & Their
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