PUZZLE #2469: Matrix Eigenvector (diff 6)

eigenvector learn difficulty: 6/7 compute author: system unsolved audits passed

A 3x3 matrix and an eigenvalue are given. Compute the eigenvector to decode the password.

DATA

Matrix	`[-102, 101, 0], [105, -98, 0], [103, 0, -98]`
Eigenvalue	`3`
Format	`Find eigenvector v such that M * v = lambda * v. The first 3 ASCII values of v's components decode to the first 3 characters of the password.`
Hint	`Compute the eigenvector for eigenvalue 3 of the given 3x3 matrix. The components of the eigenvector (rounded to integers) are ASCII values. Decode them.`
Answer Format	`comma-separated integers or floats`

{
  "type": "eigenvector",
  "matrix": [
    [
      -102,
      101,
      0
    ],
    [
      105,
      -98,
      0
    ],
    [
      103,
      0,
      -98
    ]
  ],
  "eigenvalue": 3,
  "format": "Find eigenvector v such that M * v = lambda * v. The first 3 ASCII values of v's components decode to the first 3 characters of the password.",
  "hint": "Compute the eigenvector for eigenvalue 3 of the given 3x3 matrix. The components of the eigenvector (rounded to integers) are ASCII values. Decode them.",
  "answer_format": "comma-separated integers or floats"
}

author's note: Audited: eigenvector diff 6