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Average Member

9 Posts

Posted - 03/27/2012 :  11:18:06  Show Profile  Reply with Quote
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.
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Advanced Member

299 Posts

Posted - 03/27/2012 :  11:52:06  Show Profile  Reply with Quote
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.
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