Unit Preliminary Information
Role of Lectures
- Important definitions
- Worked examples
- Common pitfalls
- Useful analogies
Introduction
Chapter 1 Goals:
- Identify linear equations
- Solve systems of linear equations
- Determine how many solutions a system has
A linear equation is an equation whose terms are numbers and variables to the first power.
A solution to a linear equation is a choice of values (numbers) for the variables that satisfies the equation.
Systems of Linear Equations
A system of linear equations (SLE) is a collection of linear equations.
A solution to an SLE must satisfy all the equations.
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We can visualise solutions to SLEs with 2 or 3 variables
- e.g. using 2D and 3D geometry to plot a line/plane
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Solutions written as:
- Variables and set are an example
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An SLE can have:
- No solutions
- Unique solution
- Infinite solutions
Theorem 1.7.
Elementary row operations change the system of linear equations but do not alter the solution set.
Keep changing an SLE into a simpler SLE
Read: Systems of Linear Equations
- Information on row echelon form
Read about leading entries on lecture slides (page 25)
No lecture next Monday (public holiday)