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.