Question

Find the determinant of the following matrix
2 -3 4
5 1 -2
10 3 -1

Answer 1

\[\left| \det \right| = 109\]

Answer 2

2(-1+6) +3(-5 + 20) + 4(15 - 10)

= 10 + 45 + 20 = 75

Answer 3

\[\left|\begin{matrix}
2&-3&4\\5&1&-2\\10&3&-1
\end{matrix}\right|=2\left|\begin{matrix}
1&-2\\3&-1
\end{matrix}\right|+3\left|\begin{matrix}
5&-2\\10&-1
\end{matrix}\right|+4\left|\begin{matrix}
5&1\\10&3
\end{matrix}\right|\]

Answer 4

i dont get how you get the matrix for 3 and 4

Answer 5

You just block out the row and the column. So, the 2 is in row one column one so you block out row one and column one. The 3 is in row one column two, so you block out row one and column two. Etc.

Answer 6

The reason it's +3 instead of -3 is, for the second column you have to subtract instead of adding. So they cancel out.

Answer 7

thanks