While on a shopping trip, you and a friend each purchase the same items, but in...

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While on a shopping trip, you and a friend each purchase the same items, but in different quantities, as follows: Case A. B. C. You buy: 3 apples and 2 bananas for $4 2 carrots and 6 dates for $7 1 eggplant and 2 fennel bulbs for $2.50 Your friend buys: 1 apple and 2 bananas for $2 3 dates and 1 carrot for $3.50 4 eggplants and 8 bulbs of fennel for $8 For each of the three cases A.-C. above: (a) Write down a linear system of equations describing the purchases, whose solution is the price of each item. (b) Write your linear system as a matrix-vector equation. (c) Determine whether or not your equation from (b) (equivalently, your linear system) has a unique solution. If so, find the solution and hence write down the cost of each item. If there is no unique solution, explain whether this is because the cashier made a mistake, or whether you do not have enough information to determine the individual costs. While on a shopping trip, you and a friend each purchase the same items, but in different quantities, as follows: Case A. B. C. You buy: 3 apples and 2 bananas for $4 2 carrots and 6 dates for $7 1 eggplant and 2 fennel bulbs for $2.50 Your friend buys: 1 apple and 2 bananas for $2 3 dates and 1 carrot for $3.50 4 eggplants and 8 bulbs of fennel for $8 For each of the three cases A.-C. above: (a) Write down a linear system of equations describing the purchases, whose solution is the price of each item. (b) Write your linear system as a matrix-vector equation. (c) Determine whether or not your equation from (b) (equivalently, your linear system) has a unique solution. If so, find the solution and hence write down the cost of each item. If there is no unique solution, explain whether this is because the cashier made a mistake, or whether you do not have enough information to determine the individual costs.

Answer rating: 100% (QA)

Okay here are the steps for each case A a System of equations 3x 2y 4 x 2y 2 Where x is the price of ... View the full answer