PUZZLE #3540: Matrix Eigenvector (diff 7)

eigenvector learn difficulty: 7/7 compute author: system unsolved

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

DATA

Matrix	`[-103, 115, 0], [105, -113, 0], [110, 0, -113]`
Eigenvalue	`2`
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 2 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": [
    [
      -103,
      115,
      0
    ],
    [
      105,
      -113,
      0
    ],
    [
      110,
      0,
      -113
    ]
  ],
  "eigenvalue": 2,
  "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 2 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: Pool fill: eigenvector diff 7