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國立政治大學 2025 · 考試 · 第 13 題

$A$ and $B$ are any matrices with the same number of rows. What can you say about the comparison of $Rank(A)$ and $Rank([A\ B])$ without any additional conditions, where $[A\ B]$ is the block matrix formed by concatenating $A$ and $B$ column-wise.

(A)
$Rank(A) \ge Rank([A\ B])$
(B)
$Rank(A) \le Rank([A\ B])$
(C)
$Rank(A) > Rank([A\ B])$
(D)
$Rank(A) = Rank([A\ B])$
(E)
$Rank(A) < Rank([A\ B])$

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