A matrix is non-invertable, or singular, when its determinant is zero.
-Dan
I have a 3x3 matrix:
1, -2, 0
k, 1, k
0, -2, 1
and I have to find all values of K that make the matrix non-invertible. I know matrices are non-invertible when 2 rows are proportionate, but (in my mind) this won't work in the matrix given because no 2 rows will be proportionate for a single k value. This answer is however marked incorrect when input in WileyPlus (online math questions thing).
If anyone has insight into if there is actually an answer and I'm missing it or can provide more insight that would be great!
cheers
Yes, it is true that "if two rows of a matrix are proportionate then the matrix is not invertible". Your error is in thinking that the converse of that, "if a matrix is not invertible, then two rows are proportionate" must be true. It isn't.
If anyone has insight into if there is actually an answer and I'm missing it or can provide more insight that would be great!
cheers