If \( M_k = \begin{bmatrix} k & k-1 \\ k-1 & k \end{bmatrix} \) where \( k \) is a natural number, then what is \( |M_1| + |M_2| + |M_3| + \dots + |M_{50}| \) equal to ?

Explanation

The determinant |M_k| expands to k^2 - (k-1)^2 = 2k - 1. Summing this from k=1 to 50 gives an AP of the first 50 odd numbers (1 + 3 + ... + 99), the sum of which is 50^2 = 2500.

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