8. The following matrix consists of a shoe store's inventory of sneakers, slippers and garden boots in sizes small, medium, and large:\begin{tabular}{|l|l|l|l|}\hline & Small & Medium & Large \\\hline Sneakers & 20 & 15 & 10 \\\hline Slippers & 30 & 25 & 18 \\\hline Garden Boots & 15 & 12 & 8 \\\hline\end{tabular}(a) Form a 3x3 matrix to represent the information given above.Sneakers sell for $150; Slippers sell for $30, and Garden Boots sell for $125.(b) Form a 1x3 matrix to represent this information.[2](c) Use matrix multiplication to determine how much the inventory is worth.
Q. 8. The following matrix consists of a shoe store's inventory of sneakers, slippers and garden boots in sizes small, medium, and large:\begin{tabular}{|l|l|l|l|}\hline & Small & Medium & Large \\\hline Sneakers & 20 & 15 & 10 \\\hline Slippers & 30 & 25 & 18 \\\hline Garden Boots & 15 & 12 & 8 \\\hline\end{tabular}(a) Form a 3x3 matrix to represent the information given above.Sneakers sell for $150; Slippers sell for $30, and Garden Boots sell for $125.(b) Form a 1x3 matrix to represent this information.[2](c) Use matrix multiplication to determine how much the inventory is worth.
Form Inventory Matrix: Form a 3x3 matrix for the inventory of sneakers, slippers, and garden boots in sizes small, medium, and large.Inventory Matrix:⎣⎡20301515251210188⎦⎤
Form Price Matrix: Form a 1x3 matrix for the prices of sneakers, slippers, and garden boots.Price Matrix:[15030125]
Calculate Total Value: Multiply the price matrix by the inventory matrix to find the total value of the inventory.Calculation:[15030125]⋅⎣⎡20301515251210188⎦⎤=[(150⋅20+30⋅30+125⋅15)(150⋅15+30⋅25+125⋅12)(150⋅10+30⋅18+125⋅8)]=[615046502900]
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