GATE 2026 AE – Question 32
If a matrix can be written as $A = uv^T$, where both $u$ and $v$ are $n$-dimensional real-valued non-zero column vectors, then the rank of the matrix $A$ is ________ (answer in integer).
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Correct answer: 1
Explanation
Every column of $uv^T$ is a multiple of $u$ ($v_j u$), so the column space is one-dimensional. The matrix is not zero, so its rank is 1.