Chapter 2.2 Flashcards
0
Q
If A is a square matrix then what can be said of its transpose?
A
det(A) = det(transpose(A))
1
Q
If A is a square matrix with a row or column of zero’s then
A
Det(A) = 0
2
Q
Let A be a square matrix, how do the row (or column) operations affect the matrix?
A
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)
3
Q
Let E be an elementary matrix, what operations yields what determinants?
A
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
4
Q
If A is a square matrix with two proportional rows or two proportional columns then
A
Det(A) = 0