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)

Ultraglide

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.