Answer:
No, this transformation is not linear. A transformation is linear if it satisfies two conditions:
1) The transformation of the sum of two vectors is equal to the sum of the transformation of each vector individually.
2) The transformation of a scalar multiple of a vector is equal to the scalar multiple of the transformation of the vector.
In this case, let's consider two vectors: V1 = ([[w_{1,1}]], [[w_{2,1}]]), and V2 = ([[w_{1,2}]], [[w_{2,2}]]).
If we apply the transformation to the sum of these vectors, we get T(V1 + V2) = T( ([[w_{1,1}]] + [[w_{1,2}]]), ([[w_{2,1}]] + [[w_{2,2}]])) = ([[w_{1,1} + w_{1,2}]], [[w_{2,1} + w_{2,2} + 2]]).
On the other hand, if we apply the transformation to each vector individually and then add them, we get T(V1) + T(V2) = ([[w_{1,1} + w_{2,1}]], [[w_{2,1} + 2]]) + ([[w_{1,2} + w_{2,2}]], [[w_{2,2} + 2]]) = ([[w_{1,1} + w_{2,1} + w_{1,2} + w_{2,2}]], [[w_{2,1} + w_{2,2} + 4]]).
Since T(V1 + V2) and T(V1) + T(V2) are not equal, the transformation is not linear.
Explanation:
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