Cambridge Additional Mathematics

Matrices (Chapter 12) 309

4 Over a long weekend holiday, a baker produced the following food

items: On Friday he baked 40 dozen pies, 50 dozen pasties, 55 dozen

rolls, and 40 dozen buns. On Saturday he baked 25 dozen pies,

65 dozen pasties, 30 dozen buns, and 44 dozen rolls. On Sunday he

baked 40 dozen pasties, 40 dozen rolls, and 35 dozen of each of pies

and buns. On Monday he baked 40 dozen pasties, 50 dozen buns,

and 35 dozen of each of pies and rolls. Represent this information

as a matrix.

MATRIX NOTATION

Consider a matrixAwhich has order m£n.

We can write

A=(aij) where i=1, 2 , 3 , ....,m

j=1, 2 , 3 , ....,n

and aij is the element in theith row,jth column.

For example, a 23 is the number in row 2 and column 3 of matrixA.

EQUALITY

Two matrices areequalif they have thesame orderandthe elements in

corresponding positions are equal.

A=B , aij=bij for alli,j.

For example, if

μ

ab

cd

¶

=

μ

wx

yz

¶

then a=w, b=x, c=y, and d=z.

MATRIX ADDITION

Thao has three stores: A, B, and C. Her stock levels for

dresses, skirts, and blouses are given by the matrix:

Store

ABC

0

@

23 41 68

28 39 79

46 17 62

1

A

dresses

skirts

blouses

Some newly ordered stock has just arrived. 20 dresses,

30 skirts, and 50 blouses must be added to the stock levels

of each store. Her stock order is given by the matrix:

0

@

20 20 20

30 30 30

50 50 50

1

A

Clearly the new levels are:

0

@

23 41 68

28 39 79

46 17 62

1

A+

0

@

20 20 20

30 30 30

50 50 50

1

A=

0

@

43 61 88

58 69 109

96 67 112

1

A

Toaddtwo matrices, they must be of thesame order, and weadd

corresponding elements.

B Matrix operations and definitions

i

μ¶

j

By convention, the

are labelled

down then across.

aij

4037 Cambridge

cyan magenta yellow black Additional Mathematics

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\CAM4037\CamAdd_12\309CamAdd_12.cdr Tuesday, 7 January 2014 6:00:47 PM BRIAN