MATH 3510 Chapter Notes - Chapter 7: Elementary Matrix, Gaussian Elimination, Row Echelon Form
Document Summary
Cofactor expansion and row or column operations can sometimes be used in combination to provide an effective method for evaluating determinants. E x a m p l e 5 row operations and cofactor expansion. Solution by adding suitable multiples of the second row to the remaining rows, we obtain. In exercises 5 9, find the determinant of the given elementary matrix by inspection. In exercises 10 17, evaluate the determinant of the given matrix by reducing the matrix to row echelon form. Answer: repeat exercises 10 13 by using a combination of row reduction and cofactor expansion, repeat exercises 14 17 by using a combination of row operations and cofactor expansion. In exercises 20 27, evaluate the determinant, given that. In exercises 30 33, confirm the identities without evaluating the determinants directly: find the determinant of the following matrix. In exercises 35 36, show that without directly evaluating the determinant.
