If M is a square matrix with a zero determinant, which of the following…
GATE · 2008 · ITModified — slightly modified from the official paper; see the solution
If M is a square matrix with a zero determinant, which of the following assertion(s) is/are correct?
(S1) At least one row of M can be represented as a linear combination of the other rows.
(S2) At least one column of M can be represented as a linear combination of the other columns.
(S3) MX = 0 has a nontrivial solution.
(S4) M has an inverse.
- A.
S3 and S2
- B.
S1 and S4
- C.
S1 and S3
- D.
S1, S2 and S3
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