Delivered energy is energy provided by a vendor, such as an electric company. For households with solar panels, windmills, wood-burning furnaces, or other on-site energy sources, only a portion of the total energy used would be delivered. The following table gives data and projections for selected years for the number of various types of U.S. households (in millions) and the delivered energy consumption per household (in millions of BTUs).

Let A be the 3 × 3 matrix representing the households data (with single-family data in row 1). Let B be the 3 × 3 diagonal matrix with diagonal entries as the delivered energy data (with 2015 data as the 1-1 entry, 2020 data as the 2-2 entry, etc.).
(a) Write A and B.
(b) Calculate AB.
(c) Interpret the 1-1 entry and the 2-3 entry of AB.
(d) Find [1 1 1] AB and interpret each entry?

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Households 2015 2020 2025 Single-family Multi-family Mobile home Delivered energy consumption 95.37 32.05 6.60 82.5 91.25 29.82 6.45 86.0 86.86 27.57 6.36 86.0 91.1