Chapter 2.2

Question 0

If A is a square matrix then what can be said of its transpose?

Answer 0

det(A) = det(transpose(A))

Question 1

If A is a square matrix with a row or column of zero’s then

Answer 1

Det(A) = 0

Question 2

Let A be a square matrix, how do the row (or column) operations affect the matrix?

Answer 2

1) Row or column multiplied with a scalar k >
det(A) > k*det(A)
2) Row or column interchanged >
det(A) > -det(A)
3) Multiple of one row or column times another >
det(A) > det(A)

Question 3

Let E be an elementary matrix, what operations yields what determinants?

Answer 3

1) Row multiplied with a scalar k >
det(E) = k
2) Two rows interchanged >
det(E) = -1
3) Multiple of one row times another >
det(E) = 1

Question 4

If A is a square matrix with two proportional rows or two proportional columns then

Answer 4

Det(A) = 0