Linear operator - basis -kernel-range-linear transformation

Question

Question:

Linear Operator - Basis -Kernel-Range-Linear Transformation.

Question (1):

Let T: R³→ R³ be a linear transformation defined by

T(x, y, z) = (x + 2y - z, y + z, x + y - 2z )

Find a basis and the dimension of ( i ) Range of T ( ii) the Kernel of T

Question (2) :

If T:R⁴ → R³ is a linear transformation defined by

T( a, b, c, d) = ( a - b + c + d, a + 2c - d, a + b + 3c - 3d ) for a, b, c, d ∈ R, then find a basis for Ker T ( i.e. Null Space of T) and Range of T.