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Question: linear algebra problem...

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Linear algebra problem.
You are interested in inviting your friends to dinner so they can get acq uainted with each other, and with y so you can have a maximum of 3 guests any one night. You are trying to comput the least your friends to have at least one dinner together in your apartment. You build a matrix where the rows are indexed by your friends, and the columns are indexed by the nights that you will entertain, where a position gets a 1 if the friend designated by the row is coming to dinner on the night designated by the column. We are going to consider several situations. our residence. Your dining room table holds at most 4 t number of nights you are going to have guests in order for any two of Suppose you consider yourself to have 6 friends. Then by simple counting show that it cannot be done in 5 nights, and by building a matrix, that it can be done in 6. Verify your claim by doing the correct multiplication. 6 Suppose now that 7 friends are available. Build the minimizing m it is. There is an additional benefit to this arrangement, what is it? verify Show that having 8 friends would not be economical by showing that it would increase your costs considerably.
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