Question

compute the determinant by cofactor expansion
[1-2 5 2]
[0 0 3 0]
[2-6-7 5]
[5 0 4 4]

Answer 1

4x4 matrix? or 1x4 matrix?

Answer 2

what do you mean?

Answer 3

\[\left[\begin{matrix}1 & -2 &5 & 2 \\ 0 &0 & 3 & 0 \\ 2 & -6 & -7 & 5 \\ 5 & 0 & 4 & 4\end{matrix}\right]\]or
[1-2 5 2]
[0 0 3 0]
[2-6-7 5]
[5 0 4 4]

Answer 4

oh sorry 4x4

Answer 5

do you know how to find the 3x3 matrix determinant?

Answer 6

let it bcome A, i'm using the 1st row, \[\left| A \right| = +1\left[\begin{matrix}0 & 3 & 0 \\ -6 & -7 & 5 \\ 0 & 4 & 4 \end{matrix}\right] -(-2)\left[\begin{matrix}0 & 3 & 0 \\ 2 & -7 & 5 \\ 5 & 4 & 4\end{matrix}\right]+5\left[\begin{matrix}0 & 0 & 0 \\ 2 & -6 & 5 \\5 & 0 & 4\end{matrix}\right]-2\left[\begin{matrix}0 & 0 & 3 \\ 2 & -6 & -7 \\ 5 & 0 & 4\end{matrix}\right]\]

Answer 7

the missing part is
3
-7
4

Answer 8

then open the bracket like the way u get the determinant of 3x3 matrix~