Suppose A is a 3 x 3 matrix whose only eigenvalues are 1= -1,0,3, and suppose B is a 4 x 4 matrix whose only eigenvalues are = -2, 2, 4. For each of the following statements, answer %3D • TRUE if the statement must be true, • FALSE if the statement must be false, or • NOT ENQUGH INFO if there is not enough given information to determine if the statement is true or false. A is invertible. B is invertible. A is diagonalizable. i. ii. iii.
Suppose A is a 3 x 3 matrix whose only eigenvalues are 1= -1,0,3, and suppose B is a 4 x 4 matrix whose only eigenvalues are = -2, 2, 4. For each of the following statements, answer %3D • TRUE if the statement must be true, • FALSE if the statement must be false, or • NOT ENQUGH INFO if there is not enough given information to determine if the statement is true or false. A is invertible. B is invertible. A is diagonalizable. i. ii. iii.
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
![Suppose A is a 3 x 3 matrix whose only eigenvalues are A = -1,0, 3, and
suppose B is a 4 x 4 matrix whose only eigenvalues are = -2, 2, 4.
For each of the following statements, answer
%3D
• TRUE if the statement must be true,
• FALSE if the statement must be false, or
• NOT ENQUGH INFO if there is not enough given information to determine if
the statement is true or false.
i.
A is invertible.
ii.
B is invertible.
A is diagonalizable.
B is diagonalizable.
iii.
iv.
V.
there exists a nonzero vector v in R4 such that Bv = v.
%3D
vi.
there exists a nonzero vector w in R' such that ||Aw|| = ||w||.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fea4942db-6497-4b90-92d5-6fda7020055a%2F14f28458-ce9f-4955-bb3f-68ce41146420%2Fgvsscde_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose A is a 3 x 3 matrix whose only eigenvalues are A = -1,0, 3, and
suppose B is a 4 x 4 matrix whose only eigenvalues are = -2, 2, 4.
For each of the following statements, answer
%3D
• TRUE if the statement must be true,
• FALSE if the statement must be false, or
• NOT ENQUGH INFO if there is not enough given information to determine if
the statement is true or false.
i.
A is invertible.
ii.
B is invertible.
A is diagonalizable.
B is diagonalizable.
iii.
iv.
V.
there exists a nonzero vector v in R4 such that Bv = v.
%3D
vi.
there exists a nonzero vector w in R' such that ||Aw|| = ||w||.
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