18 votes 18 votes A square matrix is singular whenever The rows are linearly independent The columns are linearly independent The row are linearly dependent None of the above Linear Algebra gate1987 linear-algebra matrix + – makhdoom ghaya asked Nov 8, 2016 • recategorized Apr 22, 2021 by Lakshman Bhaiya makhdoom ghaya 5.6k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 5 votes 5 votes When a row(or a column) is linearly dependent on some other rows(or columns) then it means that the particular row(or column) can be made by linear combination of other rows(or columns). So we can make this dependent row(or column) completely zero by subtracting from other rows(or columns) on which it is dependent. And so we have a zero row(or column) in the determinant and so determinant will be zero. Hence, C is the correct option. sameer_hack answered Jan 22, 2023 • selected Aug 20, 2023 by Arjun sameer_hack comment Share Follow See all 0 reply Please log in or register to add a comment.
23 votes 23 votes When the rows are linearly dependent the determinant of the matrix becomes $0$ hence in that case it will become singular matrix. Hence, C is the correct option. Habibkhan answered Nov 9, 2016 • edited Jun 11, 2018 by Milicevic3306 Habibkhan comment Share Follow See all 2 Comments See all 2 2 Comments reply sanjaysharmarose commented May 19, 2020 reply Follow Share The determinant is zero, when the columns or rows of the matrix are linearly dependent. Right???? 8 votes 8 votes rishabhgupta12 commented Apr 14, 2021 reply Follow Share yes, for either rows or column 0 votes 0 votes Please log in or register to add a comment.
0 votes 0 votes 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. Hence, C is the correct option. akshay_123 answered Sep 5, 2023 akshay_123 comment Share Follow See all 0 reply Please log in or register to add a comment.