Determinants — Test Answers

What is the value of C in the matrix equation below?

Raj 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.

What is the value of given the matrix equation below?

The table below shows the number of times the dishwasher was used in three different houses over three days. Dishwasher Use House AHouse BHouse CFriday122Saturday234Sunday223On Friday, 17.5 total gallons of water were used. On Saturday, 31.5 total gallons were used. On Sunday, 24.75 total gallons were used. What is the difference between the water use per load of the dishwasher that uses the most water and the dishwasher that uses the least water?

Which value of x makes the two matrices inverses of each other?

On a 28-question test, there are 2-point questions, 4-point questions, and 5-point questions. The test is worth a total of 100 points. There are twice as many 2-point questions as 5-point questions on the test. How many 2-point questions are on the test?

The tables below show running hours of three printers that produce greeting cards and the total number of greeting cards produced over three weeks. Number of Hours Machine Is Running Printer APrinter BPrinter CWeek 1405045Week 2455035Week 3504050 Total Cards ProducedWeek 17,950Week 27,350Week 38,700Printer B uses $15 in ink every hour. What is the ink cost for each card coming from printer B?

What are the values of c and d in the matrix subtraction below?

Jonas made the following matrix of temperatures for the first 4 days of January. He also made the following matrix of temperatures for the first 4 days of February. Which matrix shows the difference of January and February?

Jim’s family is choosing whether to go to a restaurant for lunch or for dinner. The cost of a salad is $7 at lunch and $9 at dinner. The cost of a steak is $10 at lunch and $12 at dinner. Each person will choose either a salad or a steak regardless of the mealtime. Jim calculates the food bill to be $41 if they go during lunch and $51 if they go during dinner. How many people will choose a salad?

Suppose matrix D is the inverse of matrix C. Which of the following is equal to D?

Four, two-person tennis teams played tennis matches. Ivan collected the number of points won by both players on each team and arranged the information into matrices as shown. Consider the total number of points played by each tennis team. How many teams won 60 points or less?

The table below shows the composition of three mixtures of nuts. Composition of Nut Mixtures Mixture AMixture BMixture CPecans0.600.500.75Almonds0.300.450.15Walnuts0.100.050.10Mr. Murray wants to create 100 ounces of a mixture that is 62% pecans, 30% almonds, and 8% walnuts. How will the amount of Mixture A compare to the amounts of Mixtures B and C that Mr. Murray uses?

If A and B are matrices and AB = I, which of the following represents the value of B?

Which property is shown in the matrix addition below?

Matrices A and B are shown below. What values of x and y will make the equation AB = I true?

The compositions of three powdered drink mixes are shown in the table below. Drink Mix Composition Mix AMix BMix CCitric Acid0.100.150.20Flavoring0.100.050.10Sugar0.800.800.70Xavier needs to create 100 grams of a drink mix containing 18% citric acid, 8% flavoring, and 74% sugar. How much of Mix C should he use?

Which value of y makes the two matrices inverses of each other?

A trail mix is made up of peanuts that cost p dollars per pound and dried fruit that costs d dollars per pound. A blend of pound of peanuts and pound of dried fruit costs $6.50. A blend of pound of peanuts and pound of dried fruit costs $4.50. Which matrix equation can be used to solve for the cost of 1 pound of peanuts and the cost of 1 pound of dried fruit?

What are the values of a, b, and c in the matrix addition below?