Determinants — Test Answers

Which value of D would make the equation true?

The table below shows the number of house calls three different plumbers made on three different days. Number of House Calls Plumber APlumber BPlumber CMonday288Tuesday4710Wednesday399The total amount of money earned by all three plumbers on Monday was $1,400. On Tuesday they earned a total of $1,660, and on Wednesday, they earned a total of $1,650. On Thursday, Plumber A made four house calls, Plumber B made six house calls, and Plumber C made three house calls. How much total money is earned on Thursday?

Amir encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear text code for each letter by the matrix to get a matrix that represents the encoded text. The matrix representing the encoded text is . What is the secret phrase? Determine the location of spaces after you decode the text.

The table below shows the number of different types of faucets sold over three months and the total selling price of the items. Number of Faucets Sold and Total Selling Price Kitchen SinkBathroom SinkShowerTotal Selling PriceJanuary1587$2,830February17128$3,450March242521$6,680The company makes a profit of 15% on every faucet sold. What is the profit on one shower faucet?

Given matrices G and H below, which statement is true?

A total of 165 people attended the opening night of a school play. Adults were charged $6, and children were charged $2. The total amount of money collected was $618. Which augmented matrix represents the situation?

A coach purchases 47 hats for his players and their families at a total cost of $302. The cost of a small hat is $5.50. A medium hat costs $6.00. A large hat costs $7.00. He purchases three times as many medium hats as small hats. Using matrices, how many large hats did the coach purchase?

Matrices X and Y both measure and are inverses of each other. Which matrix represents their product?

Calvin encoded a secret phrase using matrix multiplication. Using A = 1, B = 2, C = 3, and so on, he multiplied the clear text code for each letter by the matrix to get a matrix that represents the encoded text. The matrix representing the encoded text is . What is the secret phrase? Determine the location of spaces after you decode the text.

Which property is shown in the matrix addition below?

What are the values of x and y in the matrix equation below?