Let \(A=I_n+xx^\top\), where In is the n× n identity matrix and…

GATE · 2025 · DA · Data Science & AI

Let A=In+xx⊤A=I_n+xx^\top, where In is the n× n identity matrix and x∈Rnx\in\mathbb{R}^n, x⊤x=1x^\top x=1. Which of the following options is/are correct?

  1. A.

    Rank of A is n

  2. B.

    A is invertible

  3. C.

    0 is an eigenvalue of A

  4. D.

    A-1 has a negative eigenvalue

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