Name: C.ShaliM
RO.ro: I1IDOOG 2
CoiseCode: MAT2OO2
6LOE 3+TG2
Coulse t e :
AppliCodenB
of difttuntial
diffeerce eaLations
Facultyname: plof
MonícaC
(MAT200)
1+1D fhe fouuier sees
data
1MIDO062-
Dia ital AMiammert
Sholtri
Sttalmorie
O60| 120 o 2uo 30oo 360
1
upto
jor
T
lengthof InfeuVA al- 360 )l=1
HCx) aao/at,(an (Ds
nT2f bn$in OT1Z
TeD
a0/t a1 (0ST0t gcos21nt bjsin
7/tba Sina12
vohuu O-T|7/
Hcx)ao+ a^tos 0t agc0520 + bi sino +
)
9-1g0
CDS0
Cosa0
1
DiS
O
:S0 60-66 7 - 7|1212112
-)
T
ST
E5
30012
0
O.5
01S
S
8-1
as2
a
ycosvoysin YSno
1%-0.5-0S 0$66F0s65|-0sto9S|65-1-645
13D 7
4D
26
Sino| sinaolyeoso
O
60
120
ba STn
-8%-2.1
1
066 0 E6-15-015
39 291
o.C66-o.t66 06- 66 039 1 0392
|
03 0.519 173
aYCDS0-0:3
a 2 TcoS20-o
6
by-22ysne
6
S:o.113
3
ba- asip2o-b-0
.
fn)
=
(:H5 -0 3
CoS
TI
-o
1cos aT1%ctO7l3 St
1be/-0b576 Sih 17/10
O
6 df twD of the eigeo Valuls of A
nal, ffnd the thrd eqcn Valuu
6
Gfven
U
Two
60
02
and nlo find the eiqen valus off
A-
+
A
eien Valuns
arl
eajual
S
PAOpectRs
y Sum of eigen valu Cs of fA fs taac of A
)
poduct of eipen vabdes of A
TrCA)= at6+2
A
is
A
1D
(1a-0)-o(0-0)+4(0-2t)
4+16 -12
Let, dg, dz be the Clqen Values of A
dtAatd3 = 10
Adg A3 -73
(AA)
NoO
d-tds1o
AAs-1a-
0
FLoTm O )A= to-A3
Put/sbstiiute
io
/t0
,
7 -72
Ct00 td-20A3) A3=-288
A-204 +l00dat2 $8 =0
Az-2 Satisfies eq
Subtinultng dz -9 in ea,O we e
ad(
AE6 d
iopo
opio
Values of A
6,61
Ac +o Poputus af vectoAs/values if d is the
i e vaue Of ,then s
eicen Value o A
ae
tigen Values ofAa
.
Ptnd thot the Eigen
Valus and
the m a t i A 4 I
5
thal
4
paOpEdies o i
Cqiven, A
Yefqen Veciors
vett
Valiues figen Veckos
+
2
5 4
Cheap:-shsad-s3 -D
S1-trCA)= 9
9g-4r(h)
+
(O+ 4)+ (O+
1)+(30-3) -23
S3=Al9 +(D+4)-1(0-+4)+ |l-2+5) -16-++3 - )5
ffnding eiqen
1
values
3
15
O O+19
1-
usinq 6mthetic divisio
chea
15
A1
15
AsAt15-0
A-3d-5A+ 15
ACA-3)-5C4-3)
A-35,1
eipovalues are 1,3,5
fy if d-1
CA-AI)X =D
CA-T)X-0
3
/o
371t2+13
31tq+93) 43at273
-|-7-13
kowingeas
yty
73
2
(A1)
/atAt
(A-AT)X -0
CA-3I)X 0
(
- -3/
23A-15 =0
147+3
-1--313
pving eas
ntesa
X
3-1
Xg
220
3XI
2
at de3
(-AIx= D
CA-5T)x0
O
2
-1 -
-5
13
-1t1213 D
9at13-0
xeiving hese equintfton
-5+15+|
1
.1/aA
Veificadion, by three peopeties;
)Sam of Elqeo value bfimatrix
matrx
s
trace of that
AtdatAs trcA)
1+3t5 4t5+0
c99
a)
pLocduckot eipp Value of matT Ýr i3
Al
X
eqmal o
d.dg.d= [A!
t.3 5 , 15
15 15
3 icen ector ale not uniaue
As, olving mastematíc eang The vectoAs ma
difto
)
qep vctos nL m
3 ffnd
the
aewD Vectons
foner Sules upto Second
toluoo irq dnta
T
D
5
3T1/6
36
Haumonic oi
4/% 51/
43-95
35
Het
length of ntcevAl ) 2L 6T1/
n-6
FS fs
fM)
iven by
=
a0+
t
an Cos hi
bn SionT]
(anCos 2n tbn sipant
fn)= aoz +4 CDSa1t b Sin a7t ag C0$4T 4 ba sin 4
u s (28 0) +re d]5
L9-)+ubsoo (s0-L-)+Lesom(15 L1-)+9t39
9
u
9
30-L-
9930
89-
9
0 S-T0-Sg-S9-51- 5ETh)9990-993 0-
s0-
S 0-
ShLEsLss9-1e-sHe 999-0 993-0-S19-S0- tn h
O
Shh-
PLIT-9L1-E 31Pl6-131L
81-9930-993 0
9-11-9-1
999 0
g0-
g0- 9Z
999-0-0-
O
O15hos
ecUs
s0
U5 9T 500
soo
5. Deteunmine the eigen Vaus and 6onre
&pondin elgenyetons
A-11
Of the npmetic matax
D
-16 and Veuty that the fgcn Vecors
6 +31 Mutualy Othoyonal.
20 13 4
ara
A=1 20 16
20 12
S: tTCA)
=
ch ca Asid sad-s3-0
t
11t3]+13
-63
Sa trCja) =|13 4. 19-16 ,
S3 |A]=
1
20
361+333-153 56
l1(13x3-16)-20(a0x31t6 4)-16(20x 4+16X3)
11(364) 20 (64) -16 (2 88) t0935y
Novo ch e4n is |63Ah
561A-tio135
frndeng eipo vas using
Supnthctic Divisiom
63
567
-12
1a15
0136
- f0135
iidos
o
271815
-45
4-5
o1-0
iqeo Nalus1,21,45
Hhdina egen Vecto
r
ea
i) Ap-1
A-AL)x 0
8
20 161/
(CA+1I)X=0
&0
2
t
Als 016
4
to
98x1+0Xg-!67 3 0
20x1+2Ma4413 O
-l6xjt 412+40%3 #0
By &olvin4 Eans,
X=
(A-9) 7
CA-AT)X = D
CA-21I) X=D
-8 a0-16||
-16 4 3
-811+201a -j6M3 aD
201-1472-ty13 D
-16tY124473 0
Bty 6olving tauatiOTs
:
CA-AT)X3 =D -6 20-I
CA-45T) X3 = 0
90 -3 1q
4
- 26 nt&0M2-161g D
20 3212 +14Mg =0
L6t K2-1uA3 =0
o
Byseling eq's
Y3
1-
Modelmataix
P)
2
2
Cheeking Pairwipe Dthosprala
X=0 (a-2 1)
x 3 0
>(122)/-
0
=0he
x0-2-12
Hence, dAthoqUnal
Peefomed J
tuansfomrcdom
Nomallzed matrix (N)
Diagenal matrix
an be
a
fs
of fomtn) NTAN
a0 16
20 13 4
-
D-
Yo
=
-2-2J-16 4 3
-18
18
-39
7 5454
10-45 90
3t-2
-8)
O
0
a43 o
405
O
D
-
O
D
ehEo-chpoor5
O97
0
45
O0
Hence
eiqen
Vectos
skoorgO
aie
[utnally Othogona.