math3c-01-W08.. - ±ned For those de±ned enter the size of...

26. (1 pt)


- 7 - 3 - 1
0 1 - 2
- 28 - 12 - 6


Compute the rank of the above matrix
27. (1 pt)


7 4 7
7 4 3
21 12 17


Compute the rank of the above matrix
28. (1 pt) 3 x - 1 y + 9 z = 5
6 x + 3 y + 6 z = 4
8 x + 5 y + 9 z = 4
Write the above system of equations in matrix form:




*


x
y
z


=




29. (1 pt) If A =


- 4 4 3
4 - 2 - 2
0 2 3


and B =


- 1 - 2 - 1
- 3 - 3 - 4
0 2 - 2


Then 4 A + B =




and A
T
=




30. (1 pt) If A =
- 2 - i 4
i - 3 + i
and B =
3 + 3 i - 2
- 2 i 1 + i
Then AB =
and BA =
31. (1 pt) Let M =
5 4
3 5
.
Find c
1
and c
2
such that M
2
+ c
1
M + c
2
I
2
= 0, where I
2
is the
identity 2 × 2 matrix.
c
1
= ,
c
2
= .
32. (1 pt) Let M =


- 2 - 1 - 2
- 2 3 3
- 2 2 1


.
Find c
1
, c
2
, and c
3
such that M
3
+ c
1
M
2
+ c
2
M + c
3
I
3
= 0, where
I
3
is the identity 3 × 3 matrix.
c
1
= ,
c
2
= ,
c
3
= .
33. (1 pt) Compute the following product.
(
1 - 1 - 3
)


- 3 - 1
- 2 - 2
- 3 2


=
( )
34. (1 pt) If A , B , and C are 2 × 2 , 2 × 7 , and 7 × 9 matrices
respectively, determine which of the following products are de-