Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > A square matrix is singular whenever:a)The ro...
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A square matrix is singular whenever:
- a)The rows are linearly independent
- b)The columns are linearly independent
- c)The rows are linearly dependent
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
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A square matrix is singular whenever:a)The rows are linearly independe...
If the rows (or columns) of a square matrix are linearly dependent, then the determinant of matrix becomes zero.
Therefore, whenever the rows are linearly dependent, the matrix is singular.
Therefore, whenever the rows are linearly dependent, the matrix is singular.
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A square matrix is singular whenever:a)The rows are linearly independe...
Explanation:
A matrix is said to be singular if it is not invertible. That is, if its determinant is zero. There are several ways to determine if a matrix is singular, one of which is by checking its linear independence.
Linear independence means that none of the rows or columns in the matrix can be expressed as a linear combination of the other rows or columns. If a matrix has linearly dependent rows or columns, it means that there is redundancy in the information contained in the matrix, and this redundancy leads to a determinant of zero.
Therefore, the correct answer is option 'C': The rows are linearly dependent.
To further explain this, we can break down the answer into the following points:
- Definition of a singular matrix: A matrix is singular if it is not invertible, which means that its determinant is zero.
- Determining linear independence: To check if a matrix has linearly independent rows or columns, we need to look for redundancy. If one row or column can be expressed as a linear combination of the others, then the matrix has linearly dependent rows or columns.
- Relation to singularity: Linearly dependent rows or columns in a matrix lead to redundancy in the information contained in the matrix, which in turn leads to a determinant of zero. This is why a matrix with linearly dependent rows or columns is singular.
- Answer: Therefore, the correct answer to the given question is option 'C': The rows are linearly dependent.
A matrix is said to be singular if it is not invertible. That is, if its determinant is zero. There are several ways to determine if a matrix is singular, one of which is by checking its linear independence.
Linear independence means that none of the rows or columns in the matrix can be expressed as a linear combination of the other rows or columns. If a matrix has linearly dependent rows or columns, it means that there is redundancy in the information contained in the matrix, and this redundancy leads to a determinant of zero.
Therefore, the correct answer is option 'C': The rows are linearly dependent.
To further explain this, we can break down the answer into the following points:
- Definition of a singular matrix: A matrix is singular if it is not invertible, which means that its determinant is zero.
- Determining linear independence: To check if a matrix has linearly independent rows or columns, we need to look for redundancy. If one row or column can be expressed as a linear combination of the others, then the matrix has linearly dependent rows or columns.
- Relation to singularity: Linearly dependent rows or columns in a matrix lead to redundancy in the information contained in the matrix, which in turn leads to a determinant of zero. This is why a matrix with linearly dependent rows or columns is singular.
- Answer: Therefore, the correct answer to the given question is option 'C': The rows are linearly dependent.
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A square matrix is singular whenever:a)The rows are linearly independentb)The columns are linearly independentc)The rows are linearly dependentd)None of the aboveCorrect answer is option 'C'. Can you explain this answer?
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