Let . What is the sum of the entries in the first column of ?

Answer and explanation

Correct answer: B. 101

  1. Step 1: Decompose matrix as , where and .
  2. Step 2: Compute powers of : . Because is nilpotent of order and commutes with , binomial expansion terminates after two terms.
  3. Step 3: Expand : .
  4. Step 4: Sum the entries in the first column: .
Answer
101.
Why not the others: drops the identity matrix , while represents only the top entry of the column.

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