For the second, R(T)=L.
Let T: R^2->R^2. Include figures for each of the following parts.
a) Find a formula T(a,b) where T represents the projectionon the y-axis along x-axis
My Solution, (CAN SOMEONE SEE IF THIS IS RIGHT):
R(T) = Y-AXIS
N(T) = X-AXIS
T(x,y) = (0,y)
b) find a formula T(a,b) where T represents the projectin on the y-axis along the line L = {(s,s): s is in R}.
solution
T(s,y) = ( s, s)
R(T) = R^2
N(T) = {0}
is this right?
A projection along L onto the y-axis means L is the null space and the y-axis is the range. See this.
So
T(a,b) = (0,b-a)
R(T) = y-axis
N(T) = L
PS: I think the answer to problem (a) is correct.