3.2 Determinants Flashcards
1
Q
If the columns of A are _______________ , then _________
A
linearly dependent
detA=0
2
Q
det( I ) = ?
A
0
3
Q
det(AB) = ?
A
det(A)det(B)
4
Q
If A is _______ then AA(^-1)=1 then det(AA(^-1)) = ?
A
1/det(A)
5
Q
If A is a 2x2 matrix and you assume A is invertible (ad-bc=!0) then_________________
A
det(A)=ad-bc
6
Q
elementary matrix (Eij)
A
the n x n square matrix with 1’s down the diagonal and eij=1
7
Q
AEij corresponds to a ____________
A
column operation
8
Q
EijA corresponds to a ____________
A
row operation
9
Q
det(AEij) = ? det(EijA) = ?
A
det(A)
10
Q
If A is an n x n matrix; c in R; then det(cA) = ?
A
c(^n)det(A)
11
Q
Row(or column) switched; ________________
A
change the sign of the determinant
12
Q
If a column (or row) has ____________ then _____________
A
a single nonzero entry
the matrix can be collapsed
