Problem 1. (a) Consider the system x + (b – 2)y + (b² – 3)z 2.x + (2b – 3)y + (b² – 1)z 3x + (3b – 5)y + (36² – 5)z 362 – 1 262 + 7 6b2 + 7 | | For an arbitrary real number b determine whether the system has no solutions or one solution or infinitely many solutions. (b) For each b determine the rank of the 3 x 3 matrix associated with the system.

An environmental engineer wants to evaluate three different methods for disposing of nonhazardous chemical waste: land application, fluidized-bed incineration, and private disposal contract. Use the estimates below to help her determine which has the least cost at /= 15.00% per year on the basis of an annual worth evaluation. First Cost AOC per Year Salvage Value Life Land $-145000 $-86000 $23000 4 years Incineration $-760000 $-70000 $260000 6 years Contract O $-132000 O 2 years

Oo.117. Subject  :- Advance Mathematic

A company decides to change its floor plan from cubicle to open office. This will bring in a constant stream of $1,000 in extra income annually. If the company invests this extra income in an account that earns 2.5% continuously compounded interest for ten years, is it worth the change? The change in floor plan costs $7,000.