A steam plant burns two types of coal: anthracite (A) and bituminous (B). For each ton of A burned, the plant produces 27.6 millon Btu of heat, 3100 grams (g) of sulfur dioxide, and 250 g of particulate matter (solid-particle pollutants). For each ton of B burned, the plan produces 30.2 million Btu, 6400 g of sulfur dixoide, and 360 g of particulate matter.

a. How much heat does the steam plant produce when it burns x1 tons of A and x2 tons of B?

b. Suppose the output of the steam plant is described by a vector that lists the amounts of heat, sulfur dioxide, and particulate matter. Express this output as a linear combination of two vectors, assuming that the plan burns x1 tons of A and x2 tons of B.

c. [M] Over a certain time period, the steam plant produced 162 million Btu of heat, 23,610 g of sulfur dioxide, and 1623 g of particulate matter. Determine how many tons of each type of coal the steam plant must have burned. Include a vector equation as part of your solution.

{Note to Tutor: I've attached my work but I am having trouble putting the augmented matrix in part c in reduced echelon form}