Math 2270
Quiz 4
1. Consider the diagonal matrix

a 0
A= 0 b
0 0

0
0 .
c
For which values of a, b, and c is A invertible? If it is invertible, what is A−1 ?
In order to find out if A is invertible, we will go
 

..
.
1
0
0
a
0
0
  1

 

..
 0 b 0 . 0 1 0 ∼ 0
 

.
0 0 c .. 0 0 1
0
ahead and try to find its inverse:

.
 1
0 0 .. a1 0 0 
a

.
⇒ A−1 =  0
1 0 .. 0 1b 0 

0
.
0 1 .. 0 0 1c
We have found the inverse, but it only makes sense if a, b, and c are not equal to zero.
2. Find the matrix product


1 0 −1
1 2
 0 1
1  3 2
1 −1 −2
2 1
We have that

1
 0
1

0 −1
1 2
1
1  3 2
−1 −2
2 1

3
1 .
3
 

3
−1 1
0
1 = 5
3
4 .
3
−6 −2 −4
0
1
b
0

0
0 .
1
c