## worded linear algebra question related to vectors

i have a worded question which i believe i have answered correctly previously, however i was hoping for a second opinion to confirm my thoughts and refresh my memory.

q. A steam plant burns two types of coal, anthracite(A) and bitumonous(B). For each tonne of A burned, the plant produces 30 million BTU of heat, 3000grams of sulphur dioxide and 300grams of particulate matter. For each tonne of B burned the plant produces 40 million BTU of heat, 6000grams of sulphur dioxide and 400grams of particulate matter.

a) how much heat does the steam plant produce when it burns x tonnes of A and y tonnes of B?

b) suppose that the output of the steam plant is described by a vector that lists the amounts of heat, sulphur dioxide and particulate matter when x tonnes of A and y tonnes of B are burned. Express this output as a linear combination of 2 vectors.

c) over a certain period of time the plant produces 150 million BTU of heat, 24000grams of sulphur dioxide and 1500grams of particulate matter. set up an equation of the form A(vector x)=(vector b) where A and vector b have particular numberical entries, that could be used to determine how many tonnes of each type of coal were burned. do not solve the system.

any thoughts