MATH125 Lecture Notes - Lecture 28: Triangular Matrix, Row Echelon Form, Scalar Multiplication

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: Nikita

Document Summary

We will make comments about the proof of this theorem later and now we only note that the above theorem provide us with the power- ful tool of computation of determinants. The strategy of computing det a is to reduce a to an echelon form and then to use the fact that the determinant of a triangular matrix is the product of the diagonal entries. We rst create zeroes below the rst entry in the rst col- umn. By the above theorem the determinant does not change. det a = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) After this operation the determi- nant change the sign. (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) det a = . Now we see that our matrix is triangular, so to compute its determinant we must take the product of its diagonal entries. Hence we have det a = ( 1) 1 3 ( 5) = 15.