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194524 RN 2103213618 1 MT Math3
1
A =
 1 2 −1−4 −7 3
−2 −6 5

L =
1 0 0l1 1 0
l2 l3 1

U =
u1 0 0u2 u3 0
u4 l5 u6

LU =
 u1 u2 u3l1u1 l1u2 + u4 l1u3 + u5
l2u1 l2u2 + l3u4 l2u3 + l3u5 + u6
 = A
comparing both, u1 = 1 u2 = 2 u3 = −1
l1u1 = −4 l1 = −4
l1u2 + u4 = −7 u4 = 1
l1u3 + u5 = 3 u5 = −1
l2u1 = −2 l2 = −2
l2u2 + l3u4 = −6 l3 = −2
l2u2 + l3u6 = 5 ul6 = 1
L =
 1 0 0−4 1 0
−2 −2 1

1
U =
1 2 −10 1 −1
0 0 1

2
A =
1 2 −10 −7 0
0 −6 5

charactersitic equations is det(A− λI) = 0
det
1− λ 2 −10 −7− λ 0
0 −6 5− λ
 = 0
(1− λ)((λ− 5)(λ+ 7)− 0)− 2(0− 0)− 1(0− 0) = 0
λ1 = 1
λ2 = 5
λ3 = −7
Eigen vector corresponging to eigen values are found below: λ1 = 1
1− 1 2 −10 −7− 1 0
0 −6 5− 1
k1k2
k3
 = 0
2k2 − k3 = 0
−8k2 = 0
−6k2 + 4k3 = 0
K1 =
10
0

λ2 = 5
2
1− 5 2 −10 −7− 5 0
0 −6 5− 5
k1k2
k3
 = 0
−4k1 + 2k2 − k3 = 0
−12k2 = 0
−6k2 = 0
K2 =
 10
−4

λ3 = −7
1− (−7) 2 −10 −7− (−7) 0
0 −6 5− (−7)
k1k2
k3
 = 0
8k1 +...