Answer:
a = [1   3   5   7   9] and b = [12   9   6   3   1]
Step-by-step explanation:
The addition of two vectors a and b is defined as 
a + b = [13   12   11   10   10]                .... (1)
The subtraction of two vectors a and b is defined as 
a - b = [-11   - 6   - 1   4    8]                 .... (2)
After adding (1) and (2), we get
(a + b) + (a - b)= [13   12   11   10   10] + [-11   - 6   - 1   4    8]
On simplification we get
2a = [13-11   12-6   11-1   10+4   10+8]
2a = [2   6   10   14   18]
Divide both sides by 2.
a = [1   3   5   7   9]
Substitute the value of vector a in equation (1).
[1   3   5   7   9] + b = [13   12   11   10   10]
Subtract vector a from both sides.
b = [13   12   11   10   10] - [1   3   5   7   9]
On simplification we get
b = [13-1   12-3   11-5   10-7   10-9]
b = [12   9   6   3   1]
Therefore the vectors a and b are defined as a = [1   3   5   7   9] and b = [12   9   6   3   1].