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Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Number 30
![is {1, t, t2,t} for
the eigenvalues of A. Verify this statement for the case when
A is diagonalizable.
e transformation
27. Let V be R" with a basis B = {b1, ..., b,}; let W be R"
with the standard basis, denoted here by ɛ; and consider the
identity transformation I : R" → R", where I(x) = x. Find
the matrix for I relative to B and E. What was this matrix
called in Section 4.4?
28. Let V be a vector space with a basis B = {b,..., b,}, let W
be the same space V with a basis C = {c...., c,}, and let I
be the identity transformation I : V → W. Find the matrix
for I relative to B and C. What was this matrix called in
Section 4.7?
= Ax. Find a
nal.
29. Let V be a vector space with a basis B = {bj,..., b,}. Find
the B-matrix for the identity transformation I: V →V.
[M] In Exercises 30 and 31, find the B-matrix for the transforma-
tion x→ Ax where B = {b1, b2, b3}.
b1 =
Г6 -2 -2
30. А — | 3 1 -2 |,
|2 -2
Ax.
hat A is not
b1 =
1
, b2 =
1, b3 =
3
is a 3 x 3
-7 -48 -16
31. A =
1
14
6.
exist a basis
nal matrix?
-3 -45 -19
-3
-2
1, b2 =
b1 =
-3
b3
are square.
= invertible
3 for some
32. [M] LetT be the transformation whose standard matrix is
given below. Find a basis for R with the property that [ T ]R
is diagonal.
en find an
-6
9.
-3
A =
-1 -2
1
is similar
-4
4
0.
4.](https://content.bartleby.com/qna-images/question/ee22cf2f-b974-4b00-a3cf-09b388e7d65d/bdeabec3-5626-47ec-a8b5-93fe52c9160d/q92jlys_thumbnail.jpeg)
Transcribed Image Text:is {1, t, t2,t} for
the eigenvalues of A. Verify this statement for the case when
A is diagonalizable.
e transformation
27. Let V be R" with a basis B = {b1, ..., b,}; let W be R"
with the standard basis, denoted here by ɛ; and consider the
identity transformation I : R" → R", where I(x) = x. Find
the matrix for I relative to B and E. What was this matrix
called in Section 4.4?
28. Let V be a vector space with a basis B = {b,..., b,}, let W
be the same space V with a basis C = {c...., c,}, and let I
be the identity transformation I : V → W. Find the matrix
for I relative to B and C. What was this matrix called in
Section 4.7?
= Ax. Find a
nal.
29. Let V be a vector space with a basis B = {bj,..., b,}. Find
the B-matrix for the identity transformation I: V →V.
[M] In Exercises 30 and 31, find the B-matrix for the transforma-
tion x→ Ax where B = {b1, b2, b3}.
b1 =
Г6 -2 -2
30. А — | 3 1 -2 |,
|2 -2
Ax.
hat A is not
b1 =
1
, b2 =
1, b3 =
3
is a 3 x 3
-7 -48 -16
31. A =
1
14
6.
exist a basis
nal matrix?
-3 -45 -19
-3
-2
1, b2 =
b1 =
-3
b3
are square.
= invertible
3 for some
32. [M] LetT be the transformation whose standard matrix is
given below. Find a basis for R with the property that [ T ]R
is diagonal.
en find an
-6
9.
-3
A =
-1 -2
1
is similar
-4
4
0.
4.
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