The standard basis and a custom basis for are shown in the figures below.
Standard basis
Custom basis
What are the custom -coordinates of the basis vectors and ? Enter your answers as a vectors of the form <1,2>.
What are the standard -coordinates of the basis vectors and ? Enter your answers as a vectors of the form <1,2>.
Find the change of basis matrix from custom -coordinates to standard -coordinates.
Find the change of basis matrix from standard -coordinates to custom -coordinates.
Find the -coordinates of the vector . Enter your answer as a vector of the form <1,2>.
Find the -coordinates of the vector . Enter your answer as a vector of the form <1,2>.
You can earn partial credit on this problem.