Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Solve only d plz solution of ist 3 parts is provided
I need Asap
Only d
![Solution -
(a)
and
we have to
Can
i.d.
Given that
T(v₁) = 3v₁ + 0₂
T (V₂)
V₁, V₂ E B
Calculate B-matrix
express T(v.) and
B = {0,₁,0₂]
[T(U)] _ B = [ 3₁ ] [ v₁]_B
ولیا
The
=
A
B-matrix
writing
B
=
=
[TV₂]-8 = [413] [0₂]-8
-B
whose [V₁_B]
and [0₂-B) are co-ordinate vector of
2.
U, and
V₂
Sino (0₁-8] = [1₁0] and [0₂-1)=[0₁1]
(c) We have to
matrix.
Can
Standard basis
1
40₁ + 30₂2
Step 2: calculation
1
T: R²->R² and
]
3
Eigen value
of B
of T
are same as
a motrix are
Same as the
because eigenvalue of
eigenvalue of any mabix that is similas to it.
.: B. is obtained by expressing T(U₁) and 1(U₂)
in terms of basis B, So
it is similas to
mabix
that
in du ca
which is
obtain?
by standard.
basis.
fint
is calculated from
•fficient of combination
Coe
T(v₁) = 30₁ + 0₂
T(√₂) =
in du led
40₁ + 0₂ =
4 3
=> ) [A-AI ] |=
=> 1²²-6d+5=0
[A₁ = 1
=
2
T
= 5
+(U₂) in terms
/
T - matrix is: -
B = {V₁, V₂}
the eigenvalue of
express T(U₁) and T(U₂₁) in terms of
vector
a
and
b
of
eigen value
3a + b
чат зь
basis
as
T-induced
an (10)
5 = (0,1))
are the eigin values.](https://content.bartleby.com/qna-images/question/c3d83429-261f-4f1e-836d-f34d9e6aca33/626f7a07-a0d8-4ab6-9b28-5eb617f2e44b/db17sbe_processed.jpeg)
Transcribed Image Text:Solution -
(a)
and
we have to
Can
i.d.
Given that
T(v₁) = 3v₁ + 0₂
T (V₂)
V₁, V₂ E B
Calculate B-matrix
express T(v.) and
B = {0,₁,0₂]
[T(U)] _ B = [ 3₁ ] [ v₁]_B
ولیا
The
=
A
B-matrix
writing
B
=
=
[TV₂]-8 = [413] [0₂]-8
-B
whose [V₁_B]
and [0₂-B) are co-ordinate vector of
2.
U, and
V₂
Sino (0₁-8] = [1₁0] and [0₂-1)=[0₁1]
(c) We have to
matrix.
Can
Standard basis
1
40₁ + 30₂2
Step 2: calculation
1
T: R²->R² and
]
3
Eigen value
of B
of T
are same as
a motrix are
Same as the
because eigenvalue of
eigenvalue of any mabix that is similas to it.
.: B. is obtained by expressing T(U₁) and 1(U₂)
in terms of basis B, So
it is similas to
mabix
that
in du ca
which is
obtain?
by standard.
basis.
fint
is calculated from
•fficient of combination
Coe
T(v₁) = 30₁ + 0₂
T(√₂) =
in du led
40₁ + 0₂ =
4 3
=> ) [A-AI ] |=
=> 1²²-6d+5=0
[A₁ = 1
=
2
T
= 5
+(U₂) in terms
/
T - matrix is: -
B = {V₁, V₂}
the eigenvalue of
express T(U₁) and T(U₂₁) in terms of
vector
a
and
b
of
eigen value
3a + b
чат зь
basis
as
T-induced
an (10)
5 = (0,1))
are the eigin values.
![(5) Consider a linear transformation T: R² R2 and a basis B = {₁, 2} of R² with
T(7₁) = 301 + 0₂
and
T(0₂) = 401 + 302.
(a) Find the B-matrix of T.
(b) Show that the eigenvalues of the B-matrix of T are the same as the eigenvalues of the
matrix that induces T.
(c) Find the eigenvalues of the matrix that induces T.
(d) Let S = [1 ₂], find the eigenvectors of the matrix that induces T as a linear combination
of ₁ and ₂.](https://content.bartleby.com/qna-images/question/c3d83429-261f-4f1e-836d-f34d9e6aca33/626f7a07-a0d8-4ab6-9b28-5eb617f2e44b/m1nte4_processed.jpeg)
Transcribed Image Text:(5) Consider a linear transformation T: R² R2 and a basis B = {₁, 2} of R² with
T(7₁) = 301 + 0₂
and
T(0₂) = 401 + 302.
(a) Find the B-matrix of T.
(b) Show that the eigenvalues of the B-matrix of T are the same as the eigenvalues of the
matrix that induces T.
(c) Find the eigenvalues of the matrix that induces T.
(d) Let S = [1 ₂], find the eigenvectors of the matrix that induces T as a linear combination
of ₁ and ₂.
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