Determinant of a 4x4 Matrix - Check my answer please?

[Tanarif]

Homework Statement

Hey guys, I usually have no trouble with 3x3 matrices, and for a 4x4 I've a rough idea how to do it but not entirely sure if I did it correct. I've attached my attempt below with working out.

The matrix:

\begin{pmatrix} 0 & 2 & 0 & 0 \\7 & a+1 & 3 & a+1 \\1 & 0 & 2 & 0 \\ a & 1 & a-2 & 0 \end{pmatrix}

2. The attempt at a solution

My working out, question 6a here:

And the answer I got is: 2a^2 + 6a + 4

Could anyone give me a quick hand as to whether that looks right / if not, how to go about doing it? Cheers

 

[Borek]

http://www.wolframalpha.com/input/?i=det+{{0,2,0,0},{7,a+1,3,a+1},{1,0,2,0},{a,1,a-2,0}}

 

[TheoMcCloskey]

Your method and solution looks correct.