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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
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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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||.
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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