Linear algebra (linear maps)?

IIf you guys could double check my work...i can't make it to my profs office hours and the homework is due the same day as the exam. No time to find out if i have no idea what i'm doing


or not.





V is a subspace of C(R) spanned by {1,x,e^-x,cos2x,sin2x}...These are linearly independent so are a basis.





The map is d/dx :V--%26gt; V





a. determine matrix representation [d/dx] with respect to the given basis.





sooo basically


d/dx: {1,x,e^-x,cos2x, sin2x} = {0,1,-e^-x, -2sin2x, 2cos2x}





and i figured it was a 5X5 matrix with


a11=0


a22 = 1


a33 = -e^-x


a44= -2*sin 2x


a55 = 2*cos 2x....the rest all zeros








b. Determine bases for the kernel and image.





Little confused here





So the kernal is the value of 1


so the basis is


{1,0,0,0,0}





The image is the rest of the values...so


{0,x,0,0,0}


{0,0,e^-x,0,0} ........ etc





or





i'll finish off in an additional note

Linear algebra (linear maps)?
sorry