I have to determine all values of h for which A is invertible
and I really don't know what should be my first step( If anyone
could guide me through this that would be awesome. Here's the
matrix: 1 1 0 1 1 0 0 1 0 1 2h + 1 0 1 1 h You mean then that
the matrix is I see two ways to do that. One is to use the fact
that a matrix is invertible if and only if its determinant is
non-zero. The other is to row-reduce this to triangular form and
use the fact that a matrix is invertible if and only if, reduced
to triangular form, it has no zeros on its main diagonal. Since
a simple way of determining the determinant of a matrix is to
reduce to triangular form, those are essentially the same. That
will give you Now you also need to note that 1) If you "add a
multiple of one row to another" the determinant of a matrix 2)
if you "multiply one row by a number", the determinant of a
matrix is multiplied by that number. 3) if you "swap two rows",
the determinant of a matrix is multiplied by -1. Since you have
not "multiplied