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1
GATE AI 2025
MCQ (More than One Correct Answer)
+1
-0

Which of the following statements is/are correct?

A
$\mathbb{R}^n$ has a unique set of orthonormal basis vectors
B
$\mathbb{R}^n$ does not have a unique set of orthonormal basis vectors
C
Linearly independent vectors in $\mathbb{R}^n$ are orthonormal
D
Orthonormal vectors $\mathbb{R}^n$ are linearly independent
2
GATE AI 2025
MCQ (More than One Correct Answer)
+1
-0

Let $A=I_n+x x^T$, where $I_n$ is the $n \times n$ identity matrix and $x \in \mathbb{R}^n, x^T x=1$. Which of the following option is/are correct?

A
Rank of A is n
B
A is invertible
C
0 is an eigenvalue of A
D
$A^{-1}$ has a negative eigenvalue
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