Reading
- In the text, read Sections 1.1 and 1.2.
- Here are some terms that are introduced in these sections that
you should begin to become familiar with.
- linear equation
- system of linear equations or linear system
- solution for a system of linear equations
- solution set for a linear system
- augmented matrix for a system of linear equations (p4;
eventually see p32 for the term coefficient matrix)
- elementary row operations on a matrix (p 5)
- what it means for a matrix to be in row-echelon form or
reduced row-echelon form (p8)
- leading 1s (or simply leading entries) in a
row-echelon-form matrix
- the method of Gaussian elimination with back-substitution
(for solving a system of linear equations)
- the method of Gauss-Jordan elimination
- for finding the reduced row-echelon form of a given
matrix
- for solving a system of linear equations
- leading variables and free variables
- homogeneous system of linear equations
- trivial solution for a homogeneous system
- nontrivial solution for a homogeneous system
Problems
- Section 1.1 p6: 3c, 6, 7, 8, 10
- Section 1.2 p19: 4bd, 5ac, 6c, 8ad, 12ab, 21, 23, 24, 25,
32
Would you like to read more about Karl Friedrich Gauss? (His
biography is sketched on p13.). Then you might try the Math History
webpage that is maintained by St. Andrews University: http://www-history.mcs.st-and.ac.uk/~history/
Here's the particular url for their biography of Gauss: http://www-history.mcs.st-and.ac.uk/~history/Mathematicians/Gauss.html
To read about an earlier description of what we now call Gaussian
elimination, a description that appeared in China between 200BC and
100 BC, see: http://www-history.mcs.st-and.ac.uk/~history/HistTopics/Matrices_and_determinants.html
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- Alexia Sontag,
Mathematics
- Wellesley College
- Date Created: January 4, 2001
- Last Modified: January 28, 2002
- Expires: June 30, 2002