Linear transformation for matrix using Einstein convention

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I feel like I am stuck. How can I interpret the equation with Einstein summation? Here is the exercise:

you should see that r′ can be written as a linear transformation of r. This means we should be able to write r′=Ar for some matrix A.

The exercise is depicted on the picture.

I will be more than thankful if someone explains that to me in minute detail. enter image description here