Find one vector in R^3 that spans the intersection of U and W where U is the xy-plane, U={(a,b,0)}, and W is the space spanned by the vectors (1,1,1) and (1,2,3).
b) Azman needs to buy some filing cabinets to store his company’s documents. A steel cabinet costs RM 200 per unit, requires 8 square feet of floor space and holds 30 cubic feet of documents. A wooden cabinet costs RM 100 per unit, requires 12 square feet of floor space, and holds 20 cubic feet of documents. The purchase of cabinets should not exceed RM 1800 and the office has no room for more than 168 square feet of cabinets. The annual maintenance fee per steel cabinet is RM 30 and the annual maintenance fee per wooden cabinet is RM 10. His company doesn’t want to spend more than RM 240 annually for the maintenance of the cabinets.
(i) Formulate an LP model to determine how many steel cabinets and wooden cabinets are needed in order to maximize the storage volume for documents.
Given a matrix 1 4 −3 3 0 1 4 −1 2 list the numbers of the first row .Q2Solve the following : a+b+37 = 6, 2a+2b-32 = 9, a+2b-62= -4 Q3How is the determinant of A written
Consider the differential equation y"-y'-6y=0. show that the substitutions y1=y and y2=y' lead the following system:
y1'=y2, y2'=6y1+y2.
Using the method of diagonalization, solve this system and then solve the original differential equation.
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