Consider the vector add = a + b = [13 12 11 10 10] and sub = a - b = [-11 - 6 - 14 8]. Find the vector a and b.

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].