Find kerT and range T and also find their basis and dimension. Hence verify rank-nullity for the following linear transformations :

a) T: R^3-R
T(x,y,z)=x+y+z

b) T:R^3-R^3 s.t
T(x,y,z)=(x+2y-z, y+z, x+y-2z)

Question

Find kerT and range T and also find their basis and dimension. Hence verify rank-nullity for the following linear transformations :

a) T: R^3->R
     T(x,y,z)=x+y+z

b) T:R^3->R^3 s.t
     T(x,y,z)=(x+2y-z, y+z, x+y-2z)

amistre64 · Answer

just a thought, but R^3 has 3 rows, n columns
                            R^1 has 1 row, 1 column

in order to map R^3 into R^1 we would have to have T as a 3x1 matrix right?

amistre64 · Answer

a also reminds me of a plane equation; <1,1,1> dot s = 0 not that that makes things any clearer for me

anonymous · Answer

try the next question !