Do a barrel roll 999999999999999
Do a barrel roll 999999999999999. Specifically, given a vector transformation T implemented as a python function, generate a large number of pairs of random vectors and assert for all of them that their sum is preserved by T. Then, do the same thing for pairs of a scalar and a vector, and ensure that T preserves scalar multiples. To comment go to liveBook 154 EXERCISES One 2D vector transformation is reflection across the x-axis.
This transformation takes a vector and returns another one which is the mirror image with respect to the x-axis: its x-coordinate should be unchanged, and its y-coordinate should change sign. Draw two vectors and their sum, as well as the reflection of these three vectors, to demonstrate that this transformation preserves vector addition. Draw another diagram to show similarly that scalar multiplication is preserved, thereby demonstrating both criteria for linearity.
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