ATProto Browser

{
  "text": "This is why I ignore the AI Overview on Google. The query was “effect on determinant if all entries are raised to a power”.",
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        "alt": "Al Overview\n\nIf you multiply all entries of an n x n matrix by a scalar k, the determinant is multiplied by k^n. If you raise each entry of the matrix to the power of p, the determinant is also raised to the power of p.\nElaboration:\n• Multiplying by a scalar: When you multiply all entries of a matrix by a scalar k, you're effectively multiplying each row by k. Since each row multiplication affects the determinant by a factor of k, and you have n rows, the overall effect on the determinant is k^n.\n• Raising entries to a power: If you raise each entry of the matrix to the power of p, you are performing p multiplications of each entry. This is equivalent to raising each row to the power of p. Since each row multiplication affects the determinant by a factor of k^p, the overall effect on the determinant is raising the determinant to the power of p.",
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        "alt": "• Example: Consider a 2x2 matrix:\ndet[[a,b],[c,d]]\nIf you raise all entries to the power of 2: \ndet[[a^2,b^2],[c^2,d^2]]\nThe determinant would change from ad -\nbc to (ad)^2 - (bc)^2 = (ad - bc)^2.\n\nLink to Wikipedia entry for “Determinant”\n\nAI responses may include mistakes. Learn more.",
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  "createdAt": "2025-05-21T23:25:52.996Z"
}