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 v_{1} = a_{1} i + b_{1} j and v_{2} = a_{2} i + b_{2} j? That is, you want to find α an β such that

This page allows you to enter in the target vector, v, and two supposed basis vectors, v_{1} and v_{2}, 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 v_{1} = i + j and v_{2} = i + j