GATE 2017 CS (CS2) – Question 32
Let $$P=\begin{pmatrix}1&1&-1\\2&-3&4\\3&-2&3\end{pmatrix},\quad Q=\begin{pmatrix}-1&-2&-1\\6&12&6\\5&10&5\end{pmatrix}.$$ Find rank(P+Q).
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Show answer and explanation
Correct answer: 2.0 to 2.0
Explanation
The sum has rows (0,−1,−2), (8,9,10), (8,8,8). The third is the sum of the first two, so rank≤2. The upper-left 2×2 minor has determinant 0·9−(−1)·8=8≠0, so rank≥2. Hence rank is 2.