Let L be the linear operator on R? defined by L(x1, x2) = (2x1 – 3x2, x1 + 4x2)*:\\ i). Find the matrix A representing L with respect to the standard basis for R?. ii). Find the matrix B representing L with respect to S = {(1, 1), (0, 1)}. iii). Find an invertible matrix P such that B = P-'AP. \ Türkçesi: L, IR? üzerinde L(x1, ¤2) = (2æ1 – 3x2, ¤1 + 4x2)* şeklinde tanımlanan bir lineer dönüşüm olsun: i). R? nin standart tabanına göre L nin temsil matrisi A yı bulunuz. ii). S = {(1,1), (0, 1)} tabanına göre L nin temsil matrisi B yi bulunuz. ii). B = P-'AP sağlayan tersininr P matrisini bulunuz. -1 -3 ‚P 2 1 0 -3 ,B 4 A 3 [ 2 A : -3 ,B 4 3 ,P 1 1 1 -3 ,B 2 1 , Р 1 A -1 1 0 2. ,P= 2 2 -3 ‚B 4 A 3 6 7 2 -3 ,B 4 -3 ,P 1 A 6 4.
Let L be the linear operator on R? defined by L(x1, x2) = (2x1 – 3x2, x1 + 4x2)*:\\ i). Find the matrix A representing L with respect to the standard basis for R?. ii). Find the matrix B representing L with respect to S = {(1, 1), (0, 1)}. iii). Find an invertible matrix P such that B = P-'AP. \ Türkçesi: L, IR? üzerinde L(x1, ¤2) = (2æ1 – 3x2, ¤1 + 4x2)* şeklinde tanımlanan bir lineer dönüşüm olsun: i). R? nin standart tabanına göre L nin temsil matrisi A yı bulunuz. ii). S = {(1,1), (0, 1)} tabanına göre L nin temsil matrisi B yi bulunuz. ii). B = P-'AP sağlayan tersininr P matrisini bulunuz. -1 -3 ‚P 2 1 0 -3 ,B 4 A 3 [ 2 A : -3 ,B 4 3 ,P 1 1 1 -3 ,B 2 1 , Р 1 A -1 1 0 2. ,P= 2 2 -3 ‚B 4 A 3 6 7 2 -3 ,B 4 -3 ,P 1 A 6 4.
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 L be the linear operator on R? defined by L(x1, x2) = (2x1 – 3x2, ¤1+ 4x2)*:\\
i). Find the matrix A representing L with respect to the standard basis for R?.
i). Find the matrix B representing L with respect to S = {(1,1), (0, 1)}.
iii). Find an invertible matrix P such that B = P-'AP. \\
Türkçesi: L, IR? üzerinde L(x1, 22) = (2x1 – 3x2, x1 + 4x2)* şeklinde tanımlanan bir lineer dönüşüm olsun:
i). R? nin standart tabanına göre L nin temsil matrisi A yı bulunuz.
i). S = {(1,1), (0, 1)} tabanına göre L nin temsil matrisi B yi bulunuz.
ii). B = P 'AP sağlayan tersininr P matrisini bulunuz.
3]
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3
3]
,B
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1
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3]
B=
4
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A =
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,P
3
,B
4
3
,P
7
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A
=
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Transcribed Image Text:Let L be the linear operator on R? defined by L(x1, x2) = (2x1 – 3x2, ¤1+ 4x2)*:\\
i). Find the matrix A representing L with respect to the standard basis for R?.
i). Find the matrix B representing L with respect to S = {(1,1), (0, 1)}.
iii). Find an invertible matrix P such that B = P-'AP. \\
Türkçesi: L, IR? üzerinde L(x1, 22) = (2x1 – 3x2, x1 + 4x2)* şeklinde tanımlanan bir lineer dönüşüm olsun:
i). R? nin standart tabanına göre L nin temsil matrisi A yı bulunuz.
i). S = {(1,1), (0, 1)} tabanına göre L nin temsil matrisi B yi bulunuz.
ii). B = P 'AP sağlayan tersininr P matrisini bulunuz.
3]
, В
4
3
1.
3]
A
3
3]
,B
4
[:
3
‚P
1
A
2 1
3
‚B
4
1
A
,P
3]
B=
4
2
A =
2 07
1
,P
3
,B
4
3
,P
7
-1
A
=
2.
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