Consider an economy with six product-producing sectors and one non-producing sector, described by the following table, where the input is in dollars needed for $1.00 of output. In answering the following questions, you are free to use Mathematica to perform any necessary calculations. However, your written answers must clearly explain the underlying concepts, and you must meaningfully interpret your results. (a) Is the consumption matrix corresponding to this economy productive? (b) Suppose the open sector consumes $w of widgets, $2w of gizmoes, $3w of doohickies, $4w of thingamabobs, $3w of wotsamajigies and $2w of hoosywotsits. What dollar output of wotsamajigies must the economy produce in order to satisfy demand