Maths Assignments | Online Homework Help

1.   Let A = [–1 2] and B = [1 0]. Find 3A + 4B.

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A. [–3 4]
B. [2 2]
C. [–1 4]
D. [1 6]


2.   Evaluate the following determinant:

A. 76
B. 81
C. 436
D. –76


3.   Find values for the variables so that the matrices are equal.

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A. x = -2; y = -2
B. x = 1; y = -2
C. x = -2; y = 1
D. x = 1; y = 1


4.   Write the augmented matrix for the following system of equations:
9x + 5z = 8
6y + 3z = 42
3x + 8y + 2z = 66



5.   The sum of two numbers is 1 and their product is –342. Find the numbers.

A. 18 and –19
B. –18 and –19; 18 and 19
C. –18 and 19
D. –18 and 19; 18 and –19

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6.   A doctor has told a sick patient to take vitamin pills. The patient needs at least 34 units of vitamin A, at least 7 units of vitamin B, and at least 22 units of vitamin C. The red vitamin pills cost $0.10 each and contain 8 units of A, 1 unit of B, and 2 units of C. The blue vitamin pills cost $0.20 each and contain 3 units of A, 1 unit of b, and 6 units of C. How many pills should the patient take each day to minimize costs?

A. 6 red and 1 blue
B. 2 red and 5 blue
C. 7 red and 0 blue
D. 5 red and 2 blue


7.   Evaluate the following determinant:

A. –18
B. –420
C. –16
D. 420


8.   Ron attends a cocktail party (with his graphing calculator in his pocket). He wants to limit his food intake to 122g of protein, 118g of fat, and 159g of carbohydrates. According to the health conscious hostess, the marinated mushroom caps have 3g of protein, 5g of fat, and 9g of carbohydrate; the spicy meatballs have 14g of protein, 7g of fat, and 15g of carbohydrates; and the deviled eggs have 13g of protein, 15g of fat, and 6g of carbohydrates. How many of each snack can he eat to obtain his goal?

A. 9 mushrooms; 4 meatballs; 3 eggs
B. 3 mushrooms; 9 meatballs; 4 eggs
C. 4 mushrooms; 3 meatballs; 9 eggs
D. 10 mushrooms; 5 meatballs; 4 eggs
9.   Evaluate the following determinant.

A. 37
B. 28
C. –37
D. 61
10.   Use Gaussian elimination to find the complete solution to the system of equations, or state that none exists.
x + y + z = 7
x – y + 2z = 7
2x + 3z = 14

11.   Solve the following system of equations using matrices. Use Gaussian elimination with back-substitution.
x – y + 2z = 6
4x + z = 1
x + 5y + z = –19

A. {(0, 1, –4)}
B. {(0, –4, 1)}
C. {(1, 0, –4)}
D. {(1, –4, 0)}


12.   Find the dimensions of a rectangle whose perimeter is 36 feet and whose area is 56 square feet.

A. 3 feet by 15 feet
B. 5 feet by 13 feet
C. 3 feet by 13 feet
D. 4 feet by 14 feet


13.   Solve the following system by the addition method:
x + y = -9
x – y = 14

A. {(9, –11.5)}
B. {(2.5,–11.5)}
C. {(2.5,11.5)}
D. {(9, 2.5)}






15.   Evaluate the following determinant:

A. –812
B. 40
C. 27
D. –13


16.   Mrs. White wants to crochet hats and afghans for a church fundraising bazaar. She needs 6 hours to make hat and 4 hours to make an afghan, and she has no more than 54 hours available. She has material for no more than 12 items, and she wants to make at least two afghans. Let x equal the number of hats she makes and y equal the number of afghans she makes. Write a system of inequalities that describes these constraints.

A. 6+ 4y ≤ 54; x+y ≤ 12; x ≥ 2
B. 4+ 6y ≤ 54; x+y ≤ 12; x ≤ 2
C. 6+ 4y ≥ 54; x+y ≤ 12; y ≥ 2
D. 6+ 4y ≤ 54; x+y ≤ 12; y ≥ 2
17.   Use Cramer’s rule to solve the following system:
–4x – 7y + 2z = –65
–2x + 7y + 7z = 80
6x – 7y – 2z = –57

A. {(2, 9, 3)}
B. {(3, 7, 3)}
C. {(9, 3, 9)}
D. {(2, –9, –3)}


18.   Use the coding matrix



19.   Evaluate the following determinant:

A. –43
B. 11
C. 43
D. –42

20.   Write the following linear system as a matrix equation in the form AX = B, where A is the coefficient matrix and B is the constant matrix.
3x + 6y = 75
9x – 2y = 65





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