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.

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 get2a = [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 getb = [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].