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MATH 1025 Lecture Notes - System Of Linear Equations, Zero Matrix, Linear Equation


Department
Mathematics and Statistics
Course Code
MATH 1025
Professor
Carolina Benedetti

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York University
Department of Mathematics and Statistics
Math 1025.03 (Prof. H Joshi) Matrix Terminology Sept. 2012
By end of first week, students are expected to understand some basic Matrix terminology and
operations discussed in Chapter 1 of the text book. I suggest you:
Write the term / phrase
Write its meaning / Definition as given in book
Take time to understand
Construct / give an example or two, to illustrate.
Leave some space for additional explanation.
A Matrix in general.
Special Matrices:
Square Matrix, Identity Matrix, Symmetric Matrix
Diagonal Matrix,, Transpose of a Matrix Skew-
symmetric Matrix Equality of Matrices. Upper / Lower triangular
Zero matrix
Properties of Matrix Arithmetic (Theorem 1.4.1 Pg. 38).
A Linear Equation
A Linear System of Equations
Systems of Linear Equations
Coefficient Matrix of a Linear System
Augmented Matrix of a Linear System
A Solution of a Linear Equation / System
Solution set of a Linear Equation / System
Inconsistent system
Homogeneous / Non homogeneous systems
Three types of Elementary Row Operations
Row-echelon Matrix
Reduced Row-echelon Matrix
Gaussian Matrix of a given matrix
Gauss-Jordan form of a given Matrix
Words of Wisdom
1. Take your notes and do your Homework in a Notebook (not loose sheets )
2. To get an A in Linear Algebra, you need to learn how to perform (and record)
elementary row operations, correctly one at a time. If you miss more
than 3 classes in all, then it will be difficult to do “well”.
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