Determinant and constant multiple.

Question

For a determinant of a matrix to be zero, is it always necessary that atleast one row of a matrix should be a constant multiple of another?

score 2 · Accepted Answer · answered Jul 30 '17 at 08:20

2

This is not correct. Look at $$\begin{pmatrix}1&0&0\\0&1&0\\1&1&0\end{pmatrix}$$

answered Jul 30 '17 at 08:20

score 1 · Answer 2 · answered Jul 30 '17 at 11:54

1

Determinant is zero if and only if the rows are linearly dependent. This means that one of the rows is linear combination of the remaining ones. The same is true for columns.

For various conditions equivalent to $\det(A)\ne0$ see: Invertible matrix.

answered Jul 30 '17 at 11:54

Martin Sleziak

53,687

Determinant and constant multiple.

2 Answers2