Maths

mathematics.docx

QUESTION 1

1. Provide an appropriate response. Let M be a 6 × 6 matrix. Which of the following statements are true? (i) I6 M = M (ii) I6 + M = M (iii) MI6 = I6 (iv) MI6 = M

		(i), (ii), (iii), (iv)
		(i), (iii), (iv)
		(i), (iv)
		(ii), (iii)

1 points

QUESTION 2

1. Find the inverse, if it exists, for the matrix.



		The inverse does not exist.

1 points

QUESTION 3

1. Provide an appropriate response. Let A = , where d and f are nonzero constants. Find A-1.

1 points

QUESTION 4

1. Solve the problem. The perimeter of a rectangle is 38 m. If the width were doubled and the length were increased by 10 m, the perimeter would be 70 m. What are the length and width of the rectangle?

		Length: 9 m; width: 4 m
		Length: 9 m; width: 9 m
		Length: 6 m; width: 13 m
		Length: 13 m; width: 6 m

1 points

QUESTION 5

1. Solve the system by using the inverse of the coefficient matrix. -3x + y + 3z - w = -1 -x - 4y + z - 2w = -15 -4x + 3y - 3z + w = 20 3x - y - z - 2w = -6

		{(-1, 3, -2, 1)}
		{(-3, 4, -1, -1)}
		{(-1, -3, 2, -1)}
		∅

1 points

QUESTION 6

1. Provide an appropriate response. Let A = and B = . Does the matrix A + B have an inverse?

		Yes
		No

1 points

QUESTION 7

1. Find the inverse, if it exists, for the matrix.

1 points

QUESTION 8

1. Find the inverse, if it exists, for the matrix.


		The inverse does not exist.

1 points

QUESTION 9

1. Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. x + 6y = -18 -7x + 5y = 32

		{(-7, -1)}
		Cramer's rule does not apply since D = 0; ∅
		{(6, -1)}
		{(-6, -2)}

1 points

QUESTION 10

1. Find the inverse, if it exists, for the matrix.




		The inverse does not exist.

1 points

QUESTION 11

1. Solve the problem. A bookstore is having a sale. All books included in the sale have a colored sticker on them to indicate the sale price. There are green stickers, red stickers, and orange stickers. Bob, Sue, and Fred each make purchases of books that are on sale. Each row of the table gives information about the numbers of book purchases and the total cost of the purchase (before taxes). Use this information to set up a matrix equation of the form which can be solved to determine the price for each type of sale book. Solve this matrix equation to find the price of a book with an orange sticker. Use the fact that for A = , A-1 = .

		$5.08
		$5.44
		$5.33
		$5.91

1 points

QUESTION 12

1. Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. -2x - 6y - z = -18 x - 7y + 8z = 59 -4x + y + z = 1

		{(1, 8, 1)}
		{(2, 1, 8)}
		{(3, -1, 8)}
		{(2, -1, -8)}

1 points

QUESTION 13

1. Solve the system by using the inverse of the coefficient matrix. x - 2y + 3z = 11 4x + y - z = 4 2x - y + 3z = 10

		∅
		{(2, 3, 5)}
		{(-2, -3, 3)}
		{(2, -3, 1)}

1 points

QUESTION 14

1. Solve the problem. Best Rentals charges a daily fee plus a mileage fee for renting its cars. Barney was charged $90 for 3 days and , while Mary was charged $162 for 5 days and . What does Best Rental charge per day and per mile?

		$17 per day; 13¢ per mile
		$12 per day; 18¢ per mile
		$18 per day; 12¢ per mile
		$19 per day; 13¢ per mile

1 points

QUESTION 15

1. Solve the problem. A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 100 black, 110 white and 90 red wires. How many of each type of cable were made?

		20 A; 30 B; 10 C
		10 A; 30 B; 93 C
		10 A; 30 B; 20 C
		10 A; 103 B; 20 C

1 points

QUESTION 16

1. Solve the problem. A $64,000 trust is to be invested in bonds paying 6%, CDs paying 5%, and mortgages paying 10%. The bond and CD investment together must equal the mortgage investment. To earn a $4910 annual income from the investments, how much should the bank invest in bonds?

		$11,000
		$9,000
		$21,000
		$32,000

1 points

QUESTION 17

1. Use the Gauss-Jordan method to solve the system of equations. If the system has infinitely many solutions, let the last variable be the arbitrary variable. -4x - 7y - z = -67 x + 6y - 2z = 20 9x + y + z = 67

		∅
		{(6, 8, 5)}
		{(6, 5, 8)}
		{(-6, 5, 12)}

1 points

QUESTION 18

		$6.50
		$6.87
		$6.99
		$6.79

1 points

QUESTION 19

1. Find the inverse, if it exists, for the matrix.


		The inverse does not exist.

1 points

QUESTION 20

1. Decide whether or not the matrices are inverses of each other. and

		Yes
		No

1 points

QUESTION 21

1. Solve the system by using the inverse of the coefficient matrix. -4x - y - 9z = -69 -5x + 7y + 5z = 36 -9x - 5y + z = -36

		{(3, 6, 3)}
		∅
		{(3, 3, 6)}
		{(-3, 3, 6)}

1 points

QUESTION 22

1. Solve the problem. A bakery sells three types of cakes, each requiring the amount of ingredients shown. Cake I Cake II Cake III To fill its orders for these cakes, the bakery used 72 cups of flour, 48 cups of sugar, and 60 eggs. How many cakes of each type were made?

		12 Cake I; 8 Cake II; 8 Cake III
		10 Cake I; 8 Cake II; 12 Cake III
		32 Cake I; 8 Cake II; 12 Cake III
		8 Cake I; 8 Cake II; 12 Cake III

1 points

QUESTION 23

1. Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the solution set. 9x + 6y = -6 -5x + 3y = -3

		{(-1, 0)}
		{(0, 0)}
		{(0, -1)}
		Cramer's rule does not apply since D = 0; ∅

1 points

QUESTION 24

1. Decide whether or not the matrices are inverses of each other. and

		Yes
		No

1 points

QUESTION 25

1. Solve the system by using the inverse of the coefficient matrix. -5x + 3y = 8 -2x + 4y = 20

		{(-2, -6)}
		{(-6, -2)}
		{(6, 2)}
		{(2, 6)}