Give all values of h for which the matrix A fails to be invertible Can someone please help me out with this please.  I know the answer is h = 8 and I know the determinant is 21h - 168 and I even know the steps to find those answers.  For some reason this is giving me fits and I must be making silly mathematical mistakes that I keep missing.  First I have been simply using cofactor expansion and cannot come up with the correct answer. Then I used row reduction where I had a seven and two zeros in the first column.
I came up with 21h - 28 at one point and 119h + 28 at one point.
Thanks to anyone taking a look at this.  I know this is a pretty simple problem but I'm not getting something right.  I am studying for a test and fill like I am understanding everything pretty well, but this one problem is making me crazy!
First I use two row reductions.  R2 becomes R1(-2)+R2 and R3 becomes R1(-1)+R3
So I get {{7,-5,3},{0,3,-5},{0,-3,h-3}}


For three by three I typically use the the rule of Sarrus. 
You get for the determinant
$$7(-7)h + (-5)1\ 7 + 3 \ 14 \ (-8) -( 7 (-7) 3 + (-8)1 \ 7 + h14\ (-5)).$$
So 
$$-49h -35 - 336 -( -147  - 56- 70h) = 21h -168. $$
