(d) (i) State the definition of a diagonalisable matrix. (ii) Using theorems from class to justify your answer, explain why or why not the matrix B below is diagonalisable. π 3-5 0 3 T 0 2 B = -50 π -10 0 2 -10
(d) (i) State the definition of a diagonalisable matrix. (ii) Using theorems from class to justify your answer, explain why or why not the matrix B below is diagonalisable. π 3-5 0 3 T 0 2 B = -50 π -10 0 2 -10
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![(d) (i) State the definition of a diagonalisable matrix.
(ii) Using theorems from class to justify your answer, explain why or why not the matrix
B below is diagonalisable.
ㅠ 3 -5 0
3 ㅠ 0 2
-50 ㅠ -10
0
2 -10 π
2
(e) Let V = Mat2x2(C). A linear transformation T:V→V is defined by
-a
T:
· [ ] → [*
a b
c d
a].
b
Find the eigenvalues and eigenvectors of T.
(Hint: Work from the definition to find eigenvalues.)
с
-d](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5ea8dc3-9812-419a-a20e-59637a068d91%2Fedd6dc12-766e-48bf-9bd9-39278bc83a51%2Fzg94pf9_processed.png&w=3840&q=75)
Transcribed Image Text:(d) (i) State the definition of a diagonalisable matrix.
(ii) Using theorems from class to justify your answer, explain why or why not the matrix
B below is diagonalisable.
ㅠ 3 -5 0
3 ㅠ 0 2
-50 ㅠ -10
0
2 -10 π
2
(e) Let V = Mat2x2(C). A linear transformation T:V→V is defined by
-a
T:
· [ ] → [*
a b
c d
a].
b
Find the eigenvalues and eigenvectors of T.
(Hint: Work from the definition to find eigenvalues.)
с
-d
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