Find a onedimensional complex subspace M subsetof C2 such th

Find a one-dimensional complex subspace M subsetof C^2 such that R^2 intersection M =

Solution

Solution:

Let v=(1,i).Then v is vector in C^2.

Now consider the subspace M spanned by v. That is M={cv:c belongs to C}.

Since for any complex number c,cv is a complex tuple.(i.e,both entry on cv are complex numbers),M dows not contain a vector from R². Hence M intersection R² = {0}.

Also M is a one domensional subspace of C^2.