A 0 0 1 0 0 0 0 1 1 0 0 0 0 1 0 0 det a 1 b 2 r 2 r 2

A =
0 0 1 0
0 0 0 1
1 0 0 0
0 1 0 0
det( A ) = 1
B =
− 2 R
2
R
2
− 5 R
1
+ R
3
R
3
7 R
2
+ R
3
R
3
− 4 3 −1
0 0 1
0 0 − 9
det( A ) = 0
A is invertible.
A is not invertible.

3/8/2018 UW Common Math 308 Section 5.2
3. 1/1 points | Previous Answers HoltLinAlg2 5.2.017.
Suppose that
and find the determinant of the given matrix.
­8
4. 1/1 points | Previous Answers HoltLinAlg2 5.2.020.
Consider the following matrices.
Verify that
Verify that
5. 1/1 points | Previous Answers HoltLinAlg2 5.2.024.
A ) = = 4
a b c
d e f
g h i
a b c
− 2 d − 2 e − 2 f
a + g b + h c + i
A = ,
−1 6
7 5
B =
9 4
2 1
Suppose that B is a square matrix with Find each of the following.
det( A ) = = 4
a b c
d e f
g h i
a b c
− 2 d − 2 e − 2 f
a + g b + h c + i
A = ,
−1 6
7 5
B =
9 4
2 1
2/4
(a)
(b)
(c)
(d)
6. 1/1 points | Previous Answers HoltLinAlg2 5.2.028.
Partition the matrix A in order to compute det( A ).
det( B
5
) = ­32
det( B
6
) = 64
det( BB
T
) = 4
det(( B
−1
)
5
) = ­1/32
A =
− 2 0 2 0 0
1 4 1 0 0
2 0 3 0 0
0 0 0 − 2 1
0 0 0 3 2
det( A ) = 280

3/8/2018 UW Common Math 308 Section 5.2