Two-Dimensional Basis
by Mike Martin

Consider a specific vector, v = a i + b j, where i = (1, 0) and j = (0, 1). Can this vector be written as a linear combination of any two other vectors, call them v1 = a1 i + b1 j and v2 = a2 i + b2 j? That is, you want to find α an β such that

v = α v1 + β v2

This page allows you to enter in the target vector, v, and two supposed basis vectors, v1 and v2, and see just how and if this can be done.

Enter in the values of the parameters, then press the "Visualize" button.


The target vector is
  v = i + j


The two basis vectors are
  v1 = i + j
and
v2 = i + j