MATH 240 Lecture 5: Determinants

• School: University of Maryland
• Department: Mathematics
• Course: MATH 240
• Professor: Raluca Rosca

Document Summary

The determinant of a (cid:884) (cid:884) matrix, also known as det(a) or |a| is given by the following. [(cid:887) (cid:888) (cid:886) (cid:886) (cid:887) (cid:889)] (cid:890) (cid:891) (cid:882) Cover the entire first column and row up so you only see a (cid:884) (cid:884) matrix like so (cid:882) Now calculate a regular determinant like so (cid:1830)(cid:4666)(cid:1827)(cid:4667)=(cid:888)(cid:885) And that"s the first entry of our determinant. Repeat the same process with the second row. (cid:1830)(cid:4666)(cid:1827)(cid:4667)= (cid:887)(cid:883) And once more with the third column and row. And now we add or subtract the three parts together. We start with a plus, then a minus, and finally a plus again. Once again, we cover the first row and column to reduce the matrix into something easy. So the determinant of our (cid:885) (cid:885) matrix is 110. We don"t have tricks for matrices of greater than (cid:885) (cid:885) unfortunately.