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Reviewing
matrices
Clement Radcliffe,Contributor
I
will now complete the review of matrices
by giving you the solution to last
week's homework.
Homework
The position vectors of
the points A and B are ( 2 -1) and
(-1 3 ) respectively
i.
Express AB as a column vector
ii.
Another point C is such that AC =
(7 3)
iii.
Determine the coordinates of C
Solution
i.
From the following diagram
FROM
THE DIAGRAM ABOVE
The
column vector AB = (-3 4)
ALTERNATIVELY
The
following vector equation may be derived
from triangle AOB
A
O + OB =AB
Since
OA = (2 -1) ... AO = (-2 1) (OA =
- AO)
As
OB = (-1 3)
...
AB = (-2 1) + (- 1 3) = (-3 4)
ii.
See the diagram for AC
...
C is the point (9,2).
ALTERNATIVELY
Let
C = (x, y) ... The position vector
OC = (x y)
Since
AC = AO + OC
...
(7 3) = (-2 1) + (x y)
...
(x y) = (7 3) - (-2 1) = (9 2)
...
C is (9,2)
I
have chosen to review STATISTICS
with you this week. Statistics, at
this level, may be summarised as:
- Collection
of data
- Presentation
of data
-
Analysis of data
COLLECTION
OF DATA
The
usual methods are:
a)
Experiment - measuring or counting
b)
Research
c)
Interviews
METHODS
OF PRESENTATION
The
methods which are usually used are
listed as follows:
- Bar
chart or bar graph
- Data
is represented by rectangular bars
of equal width
- The
bars are usually separated
- The
area of the bar is proportional
to the quantity represented
HOMEWORK
The
number of words in each of the first
hundred sentences of a book are recorded
in the table below.
Number
of
words |
0
-10 |
11-20 |
21-30 |
31
-40 |
41
-50 |
51-60 |
61
-70 |
71
- 80 |
81-90 |
91-100 |
| Frequency |
21 |
16 |
15 |
14 |
11 |
9 |
8 |
3 |
3 |
3 |
Using
a suitable scale, represent the above
data on both a Histogram and a Frequency
Polygon.
Clement
Radcliffe is the principal of Glenmuir
High School in May Pen.
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