To find the sum of two vectors, you will add their corresponding components. Given the vectors [tex]\( \mathbf{a} = (5, -1) \)[/tex] and [tex]\( \mathbf{b} = (-1, 8) \)[/tex]:
1. Identify the components of each vector:
- Vector [tex]\( \mathbf{a} \)[/tex] has components [tex]\( a_x = 5 \)[/tex] and [tex]\( a_y = -1 \)[/tex].
- Vector [tex]\( \mathbf{b} \)[/tex] has components [tex]\( b_x = -1 \)[/tex] and [tex]\( b_y = 8 \)[/tex].
2. Add the x-components of the vectors:
[tex]\[ \text{Sum of x-components} = a_x + b_x = 5 + (-1) = 4 \][/tex]
3. Add the y-components of the vectors:
[tex]\[ \text{Sum of y-components} = a_y + b_y = -1 + 8 = 7 \][/tex]
4. Combine the results to form the resultant vector:
[tex]\[ (4, 7) \][/tex]
Thus, the sum of the given vectors [tex]\( \mathbf{a} = (5, -1) \)[/tex] and [tex]\( \mathbf{b} = (-1, 8) \)[/tex] is [tex]\( (4, 7) \)[/tex].
