1. Describe the span of the given vectors in terms of the coefficients x, y, z of a general vector b = (x,y,z) in the span. Write b as a linear combination of the given vectors.
a1=(2,2,-2), a2=(4,6,-3), a3=(4,2,-5)
2. A company meets its production schedule by operating four plants. Determine if it is possible to close one f the plants and met the production demand with only three. If it is possible, what are the feasible production schedules? Assume each plant can be operated up to 7 days per week.
The Volta Batter Company manufactures AA, A, C, and D batteries in each of four plants. The daily production (in 1000's) for the fur plants is given in the following table:
| (1000) |
Plant 1 |
Plant 2 |
Plant 3 |
Plant 4 |
| AA |
3 |
4 |
5 |
5 |
| A |
2 |
3 |
5 |
6 |
| C |
4 |
5 |
5 |
4 |
| D |
1 |
2 |
4 |
5
|