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Question
The rank of the matrix ⎡⎢⎣−41−1−1−1−17−31⎤⎥⎦ is
The rank of the matrix ⎡⎢⎣−41−1−1−1−17−31⎤⎥⎦ is
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Solution
The correct option is B 2
A = ⎡⎢⎣−41−1−1−1−17−31⎤⎥⎦
R2↔R1→⎡⎢⎣−1−1−1−41−17−31⎤⎥⎦
R2→R2−4R1R3→R3+7R1}ThenA∼⎡⎢⎣−1−1−10530−10−6⎤⎥⎦
R3→R3+2R2ThenA∼⎡⎢⎣−1−1−1053000⎤⎥⎦
Hence ρ(A)=Number of non zero rows=2
A = ⎡⎢⎣−41−1−1−1−17−31⎤⎥⎦
R2↔R1→⎡⎢⎣−1−1−1−41−17−31⎤⎥⎦
R2→R2−4R1R3→R3+7R1}ThenA∼⎡⎢⎣−1−1−10530−10−6⎤⎥⎦
R3→R3+2R2ThenA∼⎡⎢⎣−1−1−1053000⎤⎥⎦
Hence ρ(A)=Number of non zero rows=2
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