Chapter 2.1

Question 0

If A is a square matrix, what can be said of cofactor expansion?

Answer 0

Regardless of which row or column of A is chosen, the number obtained by multiplying the entries in that row or column by the corresponding cofactors and adding the resulting products will always yield the same sum.

Question 1

Def: A minor and its cofactor

Answer 1

If A is a square matrix then the minor of entry a(ij) is denoted M(ij) and is defined to be the determinant of the submatrix that remains after the i:th row and j:th column are deleted from A. The number (-1)^(i+j)*M(ij) is denoted by C(ij) and is called the cofactor of entry a(ij).

Question 2

Def: Determinant and cofactor expansion

Answer 2

If A is an nxn matrix, then the number obtained by multiplying the entries in any row with the corresponding cofactors and adding the resulting product is called the determinant of A. The sums themselves are called cofactor expansion of A.

Question 3

If A is a triangular matrix, then what can be said about det(A)?

Answer 3

Det(A) is the product of the entries on the main diagonal of the matrix, that is det(a) = a(11)a(22)…*a(nn)