Find if possible a linear transformation R^4-->R^3 so that the nullspace is [(1,2,3,4),(0,1,2,3)] and the range the solutions to x_1+x_2+x_3=0.
The Attempt at a Solution
So I thought I should start with trying to find what kind of matrix we have from the information about the nullspace we have. I start with interpreting it as:
x_1=t, x_2 = 2t+s , x_3 = 3t+2s , x_4 = t+3s . Then I'm completly stuck. Any help wuld be nice!