MATH125 Lecture 29: 29

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

Document Summary

Cramer"s rule is needed in theoretical calculations and it gives the recipe how to solve the matrix equation ax = b. However the formula is not e cient in practice and as we said it is needed for theoretical mathematics. For any n n matrix a and any vector b in rn let ai(b) be the matrix obtained from a by replacing ith column by the vector b. Theorem. (cramer"s rule) let a be an invertible matrix of size n n. For any vector b in rn the unique solution of the equation ax = b has the following entries: x1 = det a1(b) det a. 4 ] , a1(b) = [ 6 2. 5 det a = 2, det a1(b) = 40, det a2(b) = 54. Since det a = 2 = 0 the system has a unique solution. By cramer"s rule x1 = det a1(b) det a and.