Questions

Math Transition To College Math - Unit 12: Matrices

1) Define a matrix.

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2) Describe what is meant by the dimensions of a matrix.

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3) There were three special matrices mentioned in the lesson. List each with a brief description.

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4) State the dimensions of the matrix. If it is one of the special matrices mentioned in problem #3, identify as such.

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5) State the dimensions of the matrix. If it is one of the special matrices mentioned in problem #3, identify as such.

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6) State the dimensions of the matrix. If it is one of the special matrices mentioned in problem #3, identify as such.

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7) Use matrix equality to solve for “x” and “y”.

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8) Use matrix equality to solve for “x” and “y”.

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9) Use matrix equality to solve for “x” and “y”.

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10) Use matrix equality to solve for “x” and “y”.

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For the next four problems, perform the indicated operation.

11) Perform the indicated operation.

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12) Perform the indicated operation.

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13) Perform the indicated operation.

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14) Perform the indicated operation.

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15) If B represents a matrix, explain what –3B represents.

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For the next five problems, perform the matrix multiplication, if possible. If it is not possible, write “not possible”. Represent your answers the same way as done in the previous problems.

16) Perform the matrix multiplication.

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17) Perform the matrix multiplication.

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18) Perform the matrix multiplication.

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19) Perform the matrix multiplication.

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20) Perform the matrix multiplication.

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Application

21) Adrianna found that she needed to purchase 3 cans of peaches, 1 sack of flour, 1/2 dozen eggs, and 1 1/2 sacks of sugar in order to have the ingredients for a recipe. From the advertisements in the newspaper, she found the prices of each from three grocery stores. Use the information to construct matrices and use matrix multiplication to determine her grocery bill for each store. Round the answers to the nearest cent.

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For the next five problems, refer to the following problem scenario: Emily and Rachel both collect coins. Together they have a variety of coins from the 1940’s to the 1980’s. Matrix Q shows the number of each type of coin they have.

22) What are the dimensions of matrix Q?

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23) Describe the below entry by stating its value and what it represents.

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24) Which of the following matrices would be used to multiply matrix Q to determine the amount of money Emily and Rachel have for each money denomination?

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25) Use matrix multiplication to determine how much money Rachel and Emily have for the 1950’s?

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26) How much money do Rachel and Emily have all together?

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For the next four problems, refer to the following problem scenario: Mr. McGregor has 3 fruit farms. He harvests and sells apples for $26 a box, oranges for $18 a box, lemons for $32 a box, and peaches for $19 a box. Use the matrices to solve the problems.

27) How many boxes of oranges did Mr. McGregor harvest?

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28) How much did Mr. McGregor make selling just lemons?

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29) How much money did Mr. McGregor make from a) Farm 1, b) Farm 2, and c) Farm 3?

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30) What was Mr. McGregor’s total revenue from the three farms?

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