MATH122 Lecture Notes - Lecture 1: Smith Normal Form

• School: University of Regina
• Department: Mathematics
• Course: MATH122
• Professor: ?

Document Summary

Interchanging rows: multiply a row by a coefficient, add a multiple of a row to another. An inconsistent matrix is where there are no solutions, otherwise known as a row of zeroes equaling a constant. A consistent matrix is where there are infinitely many solutions, otherwise known as a row of zeroes equaling zero. Reduced row echeleon: each leading one is the only non-zero entry in its column. If entirely zero, stop: find the first column from the left and move the row to the top, create the leading 1, create zeroes under the leading one. Rank of a matrix is the number of leading ones in the rem. A homogenous system is where all the constants are all 0. N is the number of variables in the system. Every solution is a linear combination of basic solutions. 2. (a+b)+c= a+(b+c: 0 matrix, anxm+0nxm=anxm, anxm=[-aij]nxm, anxm+- anxm=onxm, anxm-bnxm= anxm+-bnxm, p(anxm+bnxm)= pa+pb.