Find a 3x3 matrix A which is not invertible, but where no two columns are multiples of each other, and no two rows are multiples of each other. (In particular, no row or column is zero.)

Question

Vocaloid · Answer

so the determinant has to be 0, what's a method to create a matrix with a determinant 0 besides making a row/column 0?

sillybilly123 · Answer

$\begin{bmatrix}
    1       & 4 & 5 \
    2       & 5 & 7 \
    3       & 6 & 9
\end{bmatrix}$

see why it's singular?  but *no two columns are multiples of each other, and no two rows are multiples of each other*

sillybilly123 · Answer

or, same idea, but dependence between *row* vectors more obvious in this one....

$\begin{bmatrix}
    1       & 2 & 3 \
    4       & 5 & 6 \
    3       & 3 & 3
\end{bmatrix}$