Consider the linear map defined on $\displaystyle R^4$ with values in $\displaystyle R^3$ given by the matrix:

A =

( 1 3 1 -2 )

( 3 9 4 -4 ) yes, this is supposed to be a matrix, i'm new

(-1 -3 -2 0 )

a) find all x e $\displaystyle R^4$ satisfying the linear equationAx=b, with

b =

( 1)

(-2)

( 4)

b) find a basis for kerA

c) Using the Rank Theorem, find the dimension of imA

This is a past paper without solutions and would really help me revise, thank you very much !