Uhuegbulem Chinonso 
MAT 204
COMPUTER SCIENCE
18/SCI01/093
0        4         3
6       -7         1
1       -3         2
1        1         2
1       -2         1
0         3       -4
1       -3         6
4        0         2
8        5         1
 
A =
B =
C =
 
 
 
i. 
1       -3         6
4        0         2
8        5         1
RANK OF A
|A|=
 
 
|A|= 1(0 - 10) +3 (4 - 16) + 6(20 - 0)
|A|= -10 - 36 + 120 = 74 IT IS NOT EQUAL TO 0; HENCE THE RANK OF A IS 3
 
ii. RANK OF B TRANSPOSE
     
1        1         0
1       -2        3
2        1        -4
|B|=
 
 
|B|= 1(8 + 3) – 1(-4 - 6) + 0(1 + 4)
|B|= 5 + 10 + 0 = 15 IT IS NOT EQUAL TO 0; HENCE THE RANK OF B TRANSPOSE IS 3
 
iii. 
1        1          9
10    - 7         3
9        2          3
RANK OF (A + C) TRANSPOSE
|A+C|=
 
 
1       10         9
1       -7         2
9        3          3
 
|A+C|T =
 
|A+C|= 1(-21 - 6) – 10(3 - 18) + 9(3 + 63)
|A+C|= -27 + 150 + 594 = 717
IT IS NOT EQUAL TO 0; HENCE THE RANK OF (A + C) TRANSPOSE IS 3
 
 
iv. RANK OF (B + C)
1         5         5
7        -9        2
1        0       -2
 
|B+C|=
 
 
|B+C|= 1(18 - 0) -5(-14 -2) + 5(0 + 9)
|B+C|= 18 + 80 + 45 = 143
IT IS NOT EQUAL TO 0; HENCE THE RANK OF (B + C) IS 3
v. RANK OF (A+B+C)
2        2        11
11    -9         4
9       5        -1
 
|A+B+C|=
 
 
| A+B+C |= 2(9 - 20) – 2(-11 - 36) + 11(55 + 81)
| A+B+C |= -22 + 94 + 1496 = 1568
IT IS NOT EQUAL TO 0; HENCE THE RANK OF (A+B + C) IS 3