Vector Multiplication Using Matrices — Unit test Answers

Hugo reflects a vector v across the line y = –x. Nemo rotates a vector v 180° counterclockwise about the origin. Which of the following vectors would have the same image for Hugo and Nemo?

Which image is a reflection over the line y = x of triangle 1?

The matrix below represents a system of equations.Which of the following describes the solution to this system of equations?

Which determinants can be used to solve for x and y in the system of linear equations below?

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?

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?

A basketball player scored 33 points during a game by shooting 1-point free throws, 2-point field goals, and 3-point field goals. The player scored 17 times. She scored 3 more 2-point field goals than 1-point free throws. The system of equations below represents the situation, where x is the number of 1-point free throws, y is the number of 2-point field goals, and z is the number of 3-point field goals. x + y + z = 17x + 2y + 3z = 33y – x = 3Which matrix and solution represents the number of 1-point free throws, 2-point field goals, and 3-point field goals the player scored?

What is the value of the element in row 1, column 1 of matrix X?

What are the values of x and z in the solution to the system of linear equations below?

Which equation can be used to solve for y-value of the solution in the system of linear equations below?

A row operation is performed on a matrix as shown below.What is the value of x?

James bought two shirts and three pairs of pants for $87. Matthew bought two pairs of pants and one shirt for $53. Assuming each pair of pants costs the same amount and each shirt costs the same amount, how much does one pair of pants cost?

A store sells almonds for $7 per pound, cashews for $10 per pound, and walnuts for $12 per pound. A customer buys 12 pounds of mixed nuts consisting of almonds, cashews, and walnuts for $118. The customer buys 2 more pounds of walnuts than cashews. The matrix below represents this situation.If the reduced row echelon form of this matrix represents the amount of each type of nut the customer buys, which statement is a possible interpretation of the results?

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?

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?