|T O P I C R E V I E W
||Posted - 03/27/2012 : 11:18:06
Consider the following transformations.
T1 : R2 -> R4 is defined by T1(x1, x2) = (0, -10 |x1|, x2, x1 + x2)
T2 : R4 -> R3 is defined by T2(x1, x2, x3, x4) = (x1 - 11 x2, x2, -10 x1)
T3 : R3 -> R4 is defined by T3(x1, x2, x3) = (x1 + x2, 0, x2, -11 x1)
T4 : R4 -> R3 is defined by T4(x1, x2, x3, x4) = (-11 + x1 + x2, x2, -10 |x1 + x2|)
1. Which of these transformations map the zero vector to the zero vector?
(T1, T2, T3) T4 do not map the zero vector because the first
vector become -11 even x1 and x2 = 0.
2. Which of these transformations are linear transformations?
T3 and T4
Is it correct.
|1 L A T E S T R E P L I E S (Newest First)
||Posted - 03/27/2012 : 11:52:06
1. Check T1 again.
A transformation, T(x) is linear if T(a+b) = T(a) + T(b) and for a scalar, k, T(kx) = kT(x). Now apply the definition to your cases.