Week 4

Question 1

What is the minor?

Answer 1

For each (i, j) entry of a A is an element Mn(R), we define the minor Mij of A to be the determinant of the (n-1) x (n -1) matrix submatrix of A found by deleting the ith row and jth column of A.

Question 2

Define the matrix of minors.

Answer 2

The matrix of minors of an n x n matrix A is the n x n matrix M whose (i,j) entry is the (i, j) minor of A.

Question 3

Define the matrix of cofactors.

Answer 3

The matrix of cofactors of an n x n matrix A is the n x n matrix C whose (i, j) entry is (-1)^i+j(Mij), where Mij is the (i, j) minor of A.

Question 4

Define the adjoint.

Answer 4

The adjoint of an n x n matrix A is the n x n matrix adj(A) that is the transpose of the matrix of cofactors of A.