MATH 2210Q Chapter Notes - Chapter 3: Parallelepiped, Volme, Laplace Expansion

• School: UConn
• Department: Mathematics
• Course: MATH 2210Q
• Professor: Arthur Parzygnat

Document Summary

Matrix is invertible if and only if its determinant is nonzero. Cofactor expansion across the d eta j1 + aj2. + jn jn eta d row - column - Choose the row or column with the most zeros to simply calculations. Thm 2: if a is a triangular matrix, then det a is the product of the entries on the main diagonal of a. Thm 3: row operations - let a be a square matrix: a. eta etb. If a multiple of one row of a is added to another row to produce a matrix b, then d. If two rows of a are interchanged to produce b, then etb eta eta. If one row of a is multiplied by k to produce b, then etb. = k d b. c: deta = ) ( 1 r ( 0 r=#of row interchanges products of pivots in u) d d when a is invertible when a is not invertible.