1.1 What Can We Expect
Reading
Chapter 1 Section 1.1 from Understanding Linear Algebra, by David Austin.
In Figure 1.1.5, there is an example of 3 planes intersecting in a point (one solution) and 3 planes having no points common to all three planes (no solutions). Can you imagine an arrangement of the 3 planes so that there are infinitely many points common to all three planes (infinitely many solutions)?
Summary:
Possible Number of Solutions of a Linear System:
- zero solutions
- one solution
- infinitely many solutions
Connecting to the next section:
Equation of a Line in the Plane: [latex]\LARGE ax+by=c[/latex]
Systems in two variables can be thought of as looking for intersections of a set of lines.
Equation of a Plane in [latex]\LARGE \mathbb{R}^3: ax+by+cz=d[/latex]:
Systems in three variables can be thought of as looking for intersections of a set of planes.
