MATH125 Lecture Notes - Lecture 16: Transpose

• School: University of Alberta
• Department: Mathematics
• Course: MATH125
• Professor: George Peschke

Document Summary

Of a (1,1)-matrix det(a) = [x] = x. = x1 det[y1 z1] + x3 2-62-06-0iji,j det(a_ij_deleted) Suppose the determinant operation on matrices of size (n,n) is defined, n cofactor11(a) + + an+1,1 d2dn (!only multiply up the diagonals!) "alternating" if 1 n, then det[c1 ci cj cn] = -det[c1 cj Linear in each column, varying one column while keeping the other ones fixed yeilds a linear function . C1, , ci-1, ci+1, , cn are fixed, 1 n, then det[c1 ci-1 x+y ci+1 cn] = det[c1 ci-1 x ci+1 cn] + det[c1 ci-1 y ci+1 cn] det[2 3 -4] det[2 3 -6] [6 3 -3] [6 3 7] det[c1 ci-1 tx ci+1 cn] If two columns of a are equal then det(a) = 0. If two rows of a are equal then det(a) = 0 if two rows/columns of a are parallel, then det(a) = 0.