Question

A Pizza shop makes pizzas in four sizes:

Small, Medium, Large and Family.

In one particular week they have recorded the number of pizzas of each size that they have sold

each day. The data is recorded in the table below:


size

Mon

Tues

Wed

Thu

Fri

Sat

Sun

Small

28

35

28

36

37

34

45

Medium

36

37

47

32

36

38

47

large

41

42

40

35

51

56

61

Family

30

33

37

33

78

76

83

a) Write the information in the table above as a 4 × 7 matrix, P


b) Write down a suitable matrix, A, that when P is multiplied by A the resulting matrix will give the number of each size of pizza sold in the week?


Calculate the matrix PA?

Answer 1

Solution.

$P= \begin{pmatrix} 28& 35& 28 &36& 37& 34 &45 \\ 36& 37 &47 &32 &36& 38 &47\\ 41& 42 &40& 35& 51& 56& 61\\ 30& 33 &39& 33& 78& 76 &83 \end{pmatrix};$

$A= \begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \end{pmatrix};$

 $PA= \begin{pmatrix} 28& 35& 28 &36& 37& 34 &45 \\ 36& 37 &47 &32 &36& 38 &47\\ 41& 42 &40& 35& 51& 56& 61\\ 30& 33 &39& 33& 78& 76 &83 \end{pmatrix}\begin{pmatrix} 1 \\ 1 \\ 1 \\ 1 \end{pmatrix}=\begin{pmatrix} 243 \\ 273 \\ 326 \\ 372 \end{pmatrix};$

$A_{1,1}=28\sdot1+ 35\sdot1+ 28 \sdot1+36\sdot1+ 37\sdot1+ 34 \sdot1+45 \sdot1 =243;$

$A_{2,1}=36\sdot1+37\sdot1+47\sdot1+32\sdot1=36\sdot1+38\sdot1+47\sdot1=273;$

$A_{3,1}=41\sdot1+42\sdot1+40\sdot1+35\sdot1+51\sdot1+56\sdot1+61\sdot1=326;$

$A_{4,1}=30\sdot1+33\sdot1+39\sdot1+33\sdot1+78\sdot1+76\sdot1+83\sdot1=372;$

Answer:$PA=\begin{pmatrix} 243 \\ 273 \\ 326 \\ 372 \end{pmatrix}.$