Section 3: Matrices

Q21. If the d is equal to

A. -11

B. -10

C. 10

D. 7

E. 11

Q22. Apples cost $3.50 per kg, bananas cost $4.20 per kg and carrots cost $1.89 per kg. Ashley buys 3 kg of apples, 2 kg of bananas and 1 kg of carrots. A matrix product to calculate the total cost of these items is

A .

B.

C.

D.

E.

Q23. The cost prices of three different electrical items in a store are $230, $290 and $310 respectively. The selling price of each of these three electrical items is 1.3 times the cost price plus a commission of $20 for the salesman. A matrix that lists the selling price of each of these three electrical items is determined by evaluating

A.

B.

C.

D.

E.

Q24. Matrix A is a 1 × 3 matrix. Matrix B is a 3 × 1 matrix. Which one of the following matrix expressions involving A and B is defined?

A.

B.

C.

D.

E.

Q25. The determinant of is equal to 9. The value of x is

A. –7

B. –4.5

C. 1

D. 4.5

E. 7

Q26. The solution to the matrix equation is

A.

B.

C.

D.

E.

Infomation for Q27 and Q28

A large population of mutton birds igrates each year to a remote island to nest and breed. There are four nesting sites on the island, A, B, C and D.

Researchers suggest that the following transition matrix can be used to predict the number of mutton birds

nesting at each of the four sites in subsequent years. An equivalent transition diagram is also given.

Q27. Two thousand eight hundred mutton birds nest at site C in 2008. Of these 2800 mutton birds, the number that nest at site A in 2009 is predicted to be

A. 560

B. 980

C. 1680

D. 2800

E. 3360

Q28. This transition matrix predicts that, in the long term, the mutton birds will

A. nest only at site A.

B. nest only at site B.

C. nest only at sites A and C.

D. nest only at sites B and D.

E. continue to nest at all four sites.

Q29. Six thousand mutton birds nest at site B in 2008. Assume that an equal number of mutton birds nested at each of the four sites in 2007. The same transition matrix applies. The total number of mutton birds that nested on the island in 2007 was

A. 6 000

B. 8 000

C. 12 000

D. 16 000

E. 24 000

Q30. Consider the linear transformation given by the matrix the basis for this transformation under, which the matrix representation is diagonal, is given by:

A. {(5,3),(1,-1)}

B. {(3,5),(1,-1)}

C. {(3,5),(-1,1)}

D. {(5,3),(-1,1)}

E. {(3,5),(-1,-1)}