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If M is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct?
S1: Each row of M can be represented as a linear combination of the other rows
S2: Each 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
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
If M is a square matrix with a zero determinant, which of the followin...
Since M has zero determinant, its rank is not full i.e. if M is of size 3*3, then its rank is not 3. So there is a linear combination of rows which evaluates to 0 i.e.

and there is a linear combination of columns which evaluates to 0 i.e.

Now any row Ri can be written as linear combination of other rows as :
 
Similar is the case for columns.
Now MX = 0 always has one solution : X = 0 (which is called trivial solution). Now if |M| = 0, then MX = 0 has non-trivial solutions also.
So (S1), (S2), and (S3) are true. So option D is correct.
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If M is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct?S1: Each row of M can be represented as a linear combination of the other rowsS2: Each column of M can be represented as a linear combination of the other columnsS3: MX = 0 has a nontrivial solutionS4: M has an inversea)S3 and S2b)S1 and S4c)S1 and S3d)S1, S2 and S3Correct answer is option 'D'. Can you explain this answer?
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If M is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct?S1: Each row of M can be represented as a linear combination of the other rowsS2: Each column of M can be represented as a linear combination of the other columnsS3: MX = 0 has a nontrivial solutionS4: M has an inversea)S3 and S2b)S1 and S4c)S1 and S3d)S1, S2 and S3Correct answer is option 'D'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about If M is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct?S1: Each row of M can be represented as a linear combination of the other rowsS2: Each column of M can be represented as a linear combination of the other columnsS3: MX = 0 has a nontrivial solutionS4: M has an inversea)S3 and S2b)S1 and S4c)S1 and S3d)S1, S2 and S3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If M is a square matrix with a zero determinant, which of the following assertion (s) is (are) correct?S1: Each row of M can be represented as a linear combination of the other rowsS2: Each column of M can be represented as a linear combination of the other columnsS3: MX = 0 has a nontrivial solutionS4: M has an inversea)S3 and S2b)S1 and S4c)S1 and S3d)S1, S2 and S3Correct answer is option 'D'. Can you explain this answer?.
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