Parametric Equations and Planar Curves

by Vincent P. Schielack (Texas A&M University) and Kirby C. Smith (Texas A&M University)

College Mathematics Journal
September, 1994

Subject classification(s): Algebra and Number Theory | Linear Algebra
Applicable Course(s): 3.8 Linear/Matrix Algebra

The author shows that the system characterized by

$x(t) = a_1 t^2 + b_1 t + c_1$
$y(t) = a_2 t^2 + b_2 t + c_2$
$z(t) = a_3 t^2 + b_3 t + c_3$

must lie in a plane. He does this with an illustrative example represented by
$x(t) = A [t^2, t, 1]^T$
where $A$ is a constant $3 \times 3$ matrix.

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Capsule Course Topic(s):
Linear Algebra | Solving Linear Systems: Visual