SQUEEZING THE MOST OUT OF CASIO
FX-570ES CALCULATOR FOR MATRIX
COMPTATION IN NUMERICAL METHODS
TAY KIM GAIK
ROSMILA ABDUL KAHAR
3RD INTERNATIONALCONFERENCE ON
SCIENCE AND MATHEMATICS EDUCATION
10-12 NOVEMBER 2009
PENANG
SQUEEZING THE MOST OUT OF CASIO FX-570ES CALCULATOR FOR
MATRIX COMPUTATION IN NUMERICAL METHODS
Tay Kim Gaik
C e n t r e for S c i e n c e Studies,
Universiti T u n H u s s e i n O n n M a l a y s i a
<[email protected]>
Rosmila Abdul-Kahar
Centre for S c i e n c e Studies,
Universiti T u n H u s s e i n O n n M a l a y s i a
<[email protected]>
Abstract
In most examinations, scientific calculator is used to do calculation. As compared to Casio fx-570MS, Casio fx570ES calculator is more users friendly. The display of the n x m matrix is more natural which is exactly in their
mathematical form. This natural textbook display will avoid confusion among students as Casio fx-570MS only
shows one line expression. In this paper, a collection of keystroke sequences is illustrated to highlight its features
of matrix computation. Once the students can utilize their calculator throughout matrix computation in numerical
methods, they can expand their ability to any other problems involving matrix in a similar pattern for any subjects
in undergraduate level.
Introduction
W h e n u s i n g calculator in a c l a s s r o o m , almost i m m e d i a t e l y in a picture o f a m i n d is a g r a p h i n g
calculator w i t h all t h e a c c e s s o r i e s a t t a c h e d to the big screen display. H o w e v e r , it is n o t practical if student
cannot b r i n g a n d u s e t h e g r a p h i n g calculator a n y w h e r e b e c a u s e it is costly, b u l k y a n d h e a v y . In an
e x a m i n a t i o n hall w i t h a large n u m b e r o f students t a k i n g n u m e r i c a l m e t h o d , o n l y a h a n d h e l d calculator is
allowed. A s f x - 5 7 0 M S calculator ( G u e r r e r o - G a r c i a & S a n t o s - P a l o m o , 2 0 0 8 ; T a y , 2 0 0 6 ) p r o m o t e s only o n e
line display a n d soon b e c o m e outdated, t h e Casio f x - 5 7 0 E S is an e v e r y d a y calculator w h i c h student can
afford to b u y . S t u d e n t s n e e d t o get t h e m a x i m u m benefit out o f this calculator. N o t to m a k e the full use of
this calculator is such a w a s t e . It can b e u s e d in a l m o s t all subjects in a u n i v e r s i t y w h i c h n e e d calculator.
With the h e l p o f C a s i o f x - 5 7 0 E S e m u l a t o r , lecturers can easily display their k e y s t r o k e s e q u e n c e s from their
laptop in the c l a s s r o o m .
In n u m e r i c a l m e t h o d , m a t r i x is u s e d in topics such as s y s t e m of linear equations, e i g e n v a l u e eigenvector, b o u n d a r y value p r o b l e m ( B V P ) in ordinary differential e q u a t i o n ( O D E ) , partial differential
equation ( P D E ) and finite e l e m e n t m e t h o d ( F E M ) . N o t to forget t h e m a n u a l calculation o f m a t r i x w h i c h
w a s introduced in linear algebra, s t u d e n t will still n e e d a step further u s i n g their calculator in solving
matrix. W i t h C a s i o f x - 5 7 0 E S calculator display o f the n x m m a t r i x exactly in their m a t h e m a t i c a l form,
students will r e d u c e t h e a m o u n t of t i m e s p e n d i n g in solving related p r o b l e m s .
Matrix
K e y s t r o k e s e q u e n c e s o f casio f x - 5 7 0 E S for the b a s i c operation of t w o m a t r i c e s , A and B .
Let
"3
2
0"
A = 2
3
1
0
1
3
Activity
Input 3x3 matrix A
"3
2
l"
B= 4
1
2
2
3
1
1
T
T
Find A + B, A - B, AxB, A , A and B .
Calculator Display
Keystroke
raisfTjLiJllJlsltsllEllsltllli)
W(D
Input 3x3 matrix B
and
m[=)(3r=](Ti(=)[3](=)
Press |AC] button to clear screen
»ll [4J(TJ(T)(TJ[3J(^(jj@(Tj@
iju [=) [ I ] ( = ] [ I ] ( D [ S ( = ) L I ] ( D
'[ 1
B
r
1
3
"
Press (ACI button to clear screen
Adding matrix A and B
e ®&mm
MatA+MatB
e
s j
e
1
3
1
a
M l
1
ftnS
B
Subtracting matrix A
andB
Press (ACI button to clear screen
ISHIFTl 14J13J [-1 |SHIFT|[4] | 4 |
N
U
3
II
D
2
-2
-1
2
MatA-MatH
BnS
B
H
Multiplying matrix A
andB
B
2
I
0
I
I
Press (ACI button to clear screen
|SHIFT| Lfl 13J IXJ lSH|FT| [4J {_4J
-2
-2
1
HatfixMatB
AnS
«
s
0
H
I
B
10
10
en
10
1
a
s
1"
Press [AC] button to clear screen
1
b b e
detCMatA)
mscaLH[=]
Checking if A" exist,
determinant is nonzero.
A"
ISHIFTl 14 1 1 3 1 | g 1 1=1
""SiBH^r
The transpose of matrix
1mft||4||8|[shir|[4]1311)1
Trn(MatA)
1
12
-D.5
O.IEEE
- 0 . 5 0. IBCG
0.19 -0.25
- 0 . 3 5 D.WEE
?.r
T
A
A,
0
An£
H
T
B
2
3
1
2
0
I
AnS
|SHIFT| [4J |_8| [SHJFTJ (4J |J] [TJ (=1
II
2
1
L
0
1
3
1
2
2
3
1
System of linear equations
Gauss Elimination
Method
Suppose the task is to solve the linear system below by Gauss Elimination method. The keystrokes
sequences in Casio fx-570ES is the same as Casio fx-570MS (Tay, 2006), therefore, the keystroke will not
be discussed:
2*; + 3 J C + 1 0 * 3 = 9
2
x + 3x, = 6
+ 7x, + x, = 2
5Xj 4x,
2
According to Tay (2006), the answer should be as
(
0.660 ")
-0.210
v
0.831
j
Student can use direct solution of 3x3 matrix using Casio fx-570ES for comparing their answer in solving
system of linear equations in numerical methods.
Activity
Entering the linear
system
Keystroke
3:axz+bx+c=a
i
IIHllW
2
0
3l
D
ru
First row
Second row
Third row
rj] ( = j (3 ( s j rjj on
d
®
(sjEiseciJiEiraisirais]
rs m m in ru i=j
Calculator Display
1:anX+bnY=Cn
2:anX+bnY+CnZ=dn
IM0DE1 L5J
,
21
2
b
1
3
2
D
3l. \ D
If
2
2
5
jlmMr
. b
II
3
b
0
0
0
C
ID
0
b D
3
"I
o
c
10
c
*
0
0
0
0
mmm
c
0
0
10
i
0
a
9
3
Od)
x=
EJ
Y=
(3
z=
242
77
"367
305
*r>7
242
c
V
=
T h e a n s w e r is
367
^
=D367
= - 0 . 2 1 0 w h i c h is the s a m e as x = - 0 . 2 1 0
305
V 367
Cholesky
' 0.660 "
' 0.660 "
J
v
0.831 ,
v
0.831 ,
Method
T o solve the s y s t e m o f linear equations b e l o w b y C h o l e s k y m e t h o d , t h e m a t r i x should be s h o w n
first as positive definite.
3
1
0
1
3
-1
0 - 1 3
v4y
r
3
In solving t h e a b o v e e q u a t i o n s u s i n g C h o l e s k y M e t h o d , m a t r i x
A-
1
1
0 ^
3
-1
m u s t be s y m m e t r i c
0 - 1 3
positive-definite. T h e o r e m : A s y m m e t r i c m a t r i x A is positive definite if a n d only if e a c h of its leading
principal s u b m a t r i c e s h a s a p o s i t i v e d e t e r m i n a n t .
Activity
det (3)=3>0
f
3 f
det
f
3
1
det 1
C a l c u l a t o r Display
Keystroke
=8>0
0
*m e ] @] ru (d
- 1 =21>0
3
-1
3
It is s h o w n that the 3 x 3 m a t r i x a b o v e is s y m m e t r i c positive-definite.
T
F r o m A = LL ,
T
solve for L a n d L .
'3
1
0
y
Activity
Compare element by
1
0^
3
-1
-1
3,
fa
=
0
N
o 'a
c
0
e
/,
6
0
c
,°
0
ad
o6
e
=
2
/3 +c
a<i
2
bd + ce
Keystroke
bd + ce
2
2
d +e +f\
C a l c u l a t o r Display
[MODE) LU |SH|FT| ^tODE) ( j j (ALPHA) [_)J 1*3 (ALPHA) [CALCJ
x =a
1AIPHA1 ICALCl
Solve for X
£
2
element a = 3,a = ?
2
a = 3,a = X
0
0
ab = \,b = ?
IALPHAI1) ] |ALPHA| 1(-)| |ALPHA| ICALCl [ 1 I
X=
1.732850808
L-R=
R
XA=1I
a = X,b
(ALPHA] [CALCJ
ft?
= A
B.57735R?R9?
3
ad = 0,d = 0
Manually
e
[ALPHAJ 1^11™) [CALCJ [ViJ |_3J | - | |AIPHA| | ( - ) | |CALC| [=J
LW3-A
I ALPHA) [sinl |ALPHA| ICALCI | ( - ) | 11 I | - r | IALPHAJ M
1=1
D=-l-B
Isinl lac'l ICALCI
M=J3-D
0
2
2
b +c =3,c
=? c = B
2
3
bd + ce = -\,d
= 0, e = - 1
e = D
2
2
2
d +e +
f
4
=3,/ = ?
g A | [MjJ [ALPHAJ [CALCJ [Vi)
|_3J
| - | [ALPHA]
2
4
f = M
F r o m LY = b, solve Y b y forward substitution:
0
= 2
0
3
4
4
/
U s i n g direct solution from C a s i o f x - 5 7 0 E S ,
f0.577
A
1.021
2.855
r
F r o m £ x = Y, solve x b y b a c k w a r d substitution:
'1.732
0
0
v
U s i n g direct solution from C a s i o f x - 5 7 0 E S ,
0.577
'0.577
0 ^
2V6
3
4
0
•1*2
4
x
2
X
/\
-I)
= 1.021
^2.855
^-0.096^
1.286
1.762
Advantages and Shortcomes of Casio fx-570ES calculator
C a s i o f x - 5 7 0 E S calculator h e l p s educators a n d students in solving n u m e r i c a l m e t h o d s . Its helps to
reduce the a m o u n t of t i m e s p e n d in solving the tasks g i v e n in t h e class. E v e n t h o u g h it is d e s i g n e d for a
system o f m a x i m u m 3 x 3 m a t r i x , it h e l p s student a lot in t h e e x a m i n a t i o n hall. F o r m o r e t h a n 3x3 matrix,
student should u s e other r e s o u r c e s s u c h as E X C E L , M A T H C A D , M A P L E , M A T L A B , M A T H E M A T I C A
or C P r o g r a m m i n g . H e n c e users can e x t e n d t h e c o n c e p t p r e s e n t e d h e r e to a s y s t e m o f n linear equations.
Conclusion
Several e x a m p l e s of solving m a t r i x in n u m e r i c a l m e t h o d s are s h o w n in this paper. A s s o m e of the
keystrokes s e q u e n c e s for C a s i o f x - 5 7 0 E S are t h e s a m e as C a s i o f x - 5 7 0 M S in t h e b o o k written b y Tay,
(2006), the steps t o s o l v e specific topic are not described. F o r future r e s e a r c h on s q u e e z i n g the m o s t out of
C a s i o f x - 5 7 0 E S calculator, m o r e t o p i c s o n n u m e r i c a l m e t h o d will b e studied.
4
References
Tay, K . G . ( 2 0 0 6 ) . How
KUiTTHO.
To Use Calculator
Casio FX-570MS
In Numerical
Methods.
B a t u Pahat: Penerbit
Guerrero-Garcia, P. & S a n t o s - P a l o m o . A . ( 2 0 0 8 , June). Squeezing
the most out of the casio fx-570ms
for
electrical/electronics
engineers. P a p e r p r e s e n t e d at t h e P r o c e e d i n g s o f t h e International Conference on
C o m p u t a t i o n a l a n d M a t h e m a t i c a l M e t h o d s in S c i e n c e and E n g i n e e r i n g , S p a i n .
Copyright Statement
C o p y r i g h t © 2 0 0 9 < T a y K i m G a i k > & < R o s m i l a A b d u l - K a h a r > . T h e authors g r a n t a n o n - e x c l u s i v e license
t o the organisers of t h e 3 C o s M E D International C o n f e r e n c e 2 0 0 9 , S E A M E O R E C S A M t o publish this
d o c u m e n t in the C o n f e r e n c e B o o k . A n y other u s a g e is p r o h i b i t e d w i t h o u t the c o n s e n t or p e r m i s s i o n o f the
author(s).
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