Let I be the linear operator on R2 defined by L i). Find the matrix A representing I with respect to S = i). S = { ii). T = { A ii). Find the matrix B representing L with respect to T iii). Find an invertible matrix P= such that B P-¹AP. = Türkçesi: L, R² üzerinde şeklinde tanımlanan bir lineer dönüşüm olsun: A I1 x1 + x2 X2 X1 X2] [][]} tabanına göre L nin temsil matrisi 4 yı bulunuz. {H}}}]}} iii). B = P-¹AP sağlayan tersi olan P matrisini bulunuz. A A = = A = 41 11 [44], 0 [ -24 [ 14 3 [ -_-23 ³].D= [2 ²7 ]-P=[(2₂²] B= ,P 14 18 0 -24 14 ,B -41 24 -41 24 }, tabanına göre I nin temsil matrisi B yi bulunuz. -24 -41 14 24 = - [² = " I1 X2 [24 -3 B = 7 2 = {[ 3 7 -1 -3 3 ³], P = [1, 2] ,P " {H}}}])} }, = x₁ + x₂ X1 X2 3 [ 1 2 2 1 -5 ¹], ·B =[²₁4] - P = =1] 1 4 1 7 0 , = B-[3, 4] -P- [8 1/2] = -1 -3
Let I be the linear operator on R2 defined by L i). Find the matrix A representing I with respect to S = i). S = { ii). T = { A ii). Find the matrix B representing L with respect to T iii). Find an invertible matrix P= such that B P-¹AP. = Türkçesi: L, R² üzerinde şeklinde tanımlanan bir lineer dönüşüm olsun: A I1 x1 + x2 X2 X1 X2] [][]} tabanına göre L nin temsil matrisi 4 yı bulunuz. {H}}}]}} iii). B = P-¹AP sağlayan tersi olan P matrisini bulunuz. A A = = A = 41 11 [44], 0 [ -24 [ 14 3 [ -_-23 ³].D= [2 ²7 ]-P=[(2₂²] B= ,P 14 18 0 -24 14 ,B -41 24 -41 24 }, tabanına göre I nin temsil matrisi B yi bulunuz. -24 -41 14 24 = - [² = " I1 X2 [24 -3 B = 7 2 = {[ 3 7 -1 -3 3 ³], P = [1, 2] ,P " {H}}}])} }, = x₁ + x₂ X1 X2 3 [ 1 2 2 1 -5 ¹], ·B =[²₁4] - P = =1] 1 4 1 7 0 , = B-[3, 4] -P- [8 1/2] = -1 -3
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Let I be the linear operator on R² defined by L
i). Find the matrix A representing I with respect to S
=
i). S = {
ii). T = {
A
A
ii). Find the matrix B representing L with respect to T
iii). Find an invertible matrix P= such that B
P-¹AP.
=
Türkçesi: L, R² üzerinde
şeklinde tanımlanan bir lineer dönüşüm olsun:
([3],[3])
(0.8)
iii). B = P-¹AP sağlayan tersi olan P matrisini bulunuz.
A
A
=
=
A =
[
[
-23 3
14 18
14
7
41 11
[41 4], ,B
I1
X2
B=
=
} tabanına göre L nin temsil matrisi A yı bulunuz.
=
}, tabanına göre I nin temsil matrisi B yi bulunuz.
- [²
x1 + x2
X1 X2]
[24 -3
7 2
21
X2
- [82] P=[(32]
0
3
-1
=
{[
-24-4B-₁ 3-²-[3]
в =
=
2
-1
{H}}}])}
},
7
x₁ + x₂
X1
X2
3
³], P = [1, 2]
7
0 1/2
[
24 24-8-3, 3-²-4
B =
=
14
3/2
-41
2
1
1 -5
- 24 - 4 ]. B = [² ²¹ ] P = || ]
14
24
1
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb33587ae-5086-47d0-8e94-47a3042a125e%2F72049f53-0553-4a5c-91a3-733419fc5881%2Fik8q1c_processed.png&w=3840&q=75)
Transcribed Image Text:Let I be the linear operator on R² defined by L
i). Find the matrix A representing I with respect to S
=
i). S = {
ii). T = {
A
A
ii). Find the matrix B representing L with respect to T
iii). Find an invertible matrix P= such that B
P-¹AP.
=
Türkçesi: L, R² üzerinde
şeklinde tanımlanan bir lineer dönüşüm olsun:
([3],[3])
(0.8)
iii). B = P-¹AP sağlayan tersi olan P matrisini bulunuz.
A
A
=
=
A =
[
[
-23 3
14 18
14
7
41 11
[41 4], ,B
I1
X2
B=
=
} tabanına göre L nin temsil matrisi A yı bulunuz.
=
}, tabanına göre I nin temsil matrisi B yi bulunuz.
- [²
x1 + x2
X1 X2]
[24 -3
7 2
21
X2
- [82] P=[(32]
0
3
-1
=
{[
-24-4B-₁ 3-²-[3]
в =
=
2
-1
{H}}}])}
},
7
x₁ + x₂
X1
X2
3
³], P = [1, 2]
7
0 1/2
[
24 24-8-3, 3-²-4
B =
=
14
3/2
-41
2
1
1 -5
- 24 - 4 ]. B = [² ²¹ ] P = || ]
14
24
1
4
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