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Trigonometry/PrecalculusNameDeterminants of MatricesDateDay _______BlockFind the determinant for each of the following matrices.3371850762006)8)06)8)-571501416055)7)05)7)333375032385010)12)0010)12)-1047753143259)11)009)11)Write a system of equations for each of the following, then practice solving using each of the given techniques.13) A theater’s maximum capacity is 900 people. For a show, tickets were sold for $2.50 for children, $4 for students and $5.50 for adults. There were half as many adults as the number of children and students combined on a night when the theater was full. If the total profits from the night was $3,825, how many of each ticket were sold?a) Write a system of equations to represent ticket sales.b) Write a matrix equation to represent this system.c) Use an inverse matrix to find the amount of each tickets sold at the theater. (show your work!)14) Beatrice needs to buy 16 pies for an event. Apple pies cost $5, berry pies cost $4.50 and chocolate cream pies cost $5.50. Chocolate cream pies are so popular at her events, that she decides to buy as many chocolate pies as the number of apple and berry pies combined. If she has $82 to spend, how many of each pie can she buy?a) Write a system of equations to represent the number of each type of pie.b) Write an augmented matrix to represent your system of equations.c) Put your matrix into row echelon form then use back substitution to solve for the number of each pie.15) Noah has a $1500 budget to buy animals to start a small farm. He wished to buy chickens, goats and sheep. Chickens cost $20 each, goats cost $30 each, and sheep cost $50 each. He decides that the number of chickens should equal the number of goats. If he buys 50 animals in total, how many of each did he buy?a) Write a system of equations to represent the number of each type of animal.b) Write an augmented matrix to represent your system of equations.c) Solve your system of equations by putting your matrix in reduced row echelon form. (you can use your calculator!)16) Heather throwing a birthday party for her son and has a $76 budget for food and drinks. Cases of water at Costco cost $4 each, pizzas cost $10 and cakes cost $18. The number of pizzas ordered is 1 more than twice the number of cases of water she buys. If she buys 8 items total, how many of each item did she purchase?a) Write a system of equations to represent the number of each item.b) Write a matrix equation to represent your system of equations.c) Use inverse matrices to solve for the number of items purchased at Costco. Show your process!Multiply if possible. If multiplication is not possible, say “not possible” and explain why. ................
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