Question

Use matrix methods to solve the problem.

To use space effectively, librarians like to fill shelves completely. One 105-inch shelf can hold 3 dictionaries, 5 atlases, and 1 thesaurus; or 6 dictionaries and 2 thesauruses; or 2 dictionaries, 4 atlases, and 3 thesauruses. How wide is one copy of each book?
dictionaries ____ in
atlases ______ in
thesauruses _____ in

Answer 1

3 d + 5 a + 1 t = 105
6 d + 0 a + 2 t = 105
2 d + 4 a + 3 t = 105

that zero in the middle will help
coef matrix
| 3 5 1 |
| 6 0 2 | = 20+24-24-90 = -70 det
| 2 4 3 |

| 105 5 1 |
| 105 0 2 | is the same as
| 105 4 3 |

| 1 5 1 |
| 1 0 2 |times 105 = 105(10+4-8-15)=-945
| 1 4 3 |

so dictionaries = -945/-70 = 13.5
I will let you do a and t :)