我想問三階行列式點樣計

Determinants of 3-by-3 matrices
The 3×3 matrix


圖片參考：http://upload.wikimedia.org/math/d/f/7/df764e5be6abb3a0686459d3ee5b8a5b.png

has determinant


圖片參考：http://upload.wikimedia.org/math/4/1/b/41b71b302ddb9140ce63cb4d8d7e0714.png

This is just


圖片參考：http://upload.wikimedia.org/math/8/9/7/897de70c13c2ec5542679a744f53e1b6.png

which can be remembered the sum of the products of three diagonal north-west to south-east lines of matrix elements, minus the products of three diagonal south-west to north-east lines of elements when the copies of the first two columns of the matrix are written beside it as below:


圖片參考：http://upload.wikimedia.org/math/c/e/6/ce6f9a10a845f5012cb1d3d93db1e24b.png

Note that this mnemonic does not carry over into higher dimensions.