Using matrix multiplication, compute AB. This matrix directly provides the amounts of basic commodities needed for given amounts of final goods.

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PROBLEM 5 (WITH APPLICATION): NOTE: You can ignore the application if it is confusing you; the point was to provide some example of how matrix multiplication might be useful, but it has no bearing on the operations you need to perform. A fictitious factory uses 4 kinds of basic commodities, b1,b2,b3,b4 to produce 3 kinds of intermediate goods, m1,m2,m3, which in turn are used to produce 3 kinds of final products, f1,f2,f3. The matrices: AB=120101111112=124232112 provide the amount of basic commodities needed for a given amount of intermediate goods, and the amount of intermediate goods needed for a given amount of final products, respectively. For example, to produce one unit of intermediate good m1, one unit of basic commodity b1, two units of b2, no units of b3, and one unit of b4 are needed, corresponding to the first column of A