1. The problem statement, all variables and given/known data For the linear transformation T: R4 --> R3 defined by TA: v -->Av find a basis for the Kernel of TA and for the Image of of TA where A is 2 4 6 2 1 3 -4 1 4 10 -2 4 2. Relevant equations Let v = a1 b1 c1 a2 b2 c2 a3 b3 c3 a4 b4 c4 3. The attempt at a solution so v is a 4x3 matrix, and Ker(T) would just be the solution for Av = 0. I was unsure as to what the Image would be give by. Is it the matrix 2a1+4b1+6c1+2d1, 2a2+4b2+6c2+2d2, 2a3+4b3+6c3+2d3, 1a1+3b1-4c1+d1, ... etc (just the general solution of the multiplication) Which generalizes to 2 0 2 0 1 2 so the basis is [1, 2, -1] How would I find a basis for the Kernel?