Author 
Topic 

Manu
Average Member
Australia
9 Posts 
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.



Ultraglide
Advanced Member
Canada
299 Posts 
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. 



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