← Linear Algebra

How to solve

Expand along the top row: each entry times its 2×2 minor, with alternating signs + − +.

Steps

  1. Cross out row and column of each top-row entry to get its 2×2 minor.
  2. Multiply entry × det(minor), with signs +, −, +.
  3. Add the three terms.

Example

det [[2, 0, 1], [1, 3, 0], [0, 1, 1]]

  1. 2·det[[3,0],[1,1]] = 2·3 = 6.
  2. −0·(…) = 0.
  3. +1·det[[1,3],[0,1]] = 1·1 = 1. Total 7.

Answer: 7

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