MATH SOLVE

4 months ago

Q:
# 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.

Accepted Solution

A:

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].