A is an nxn matrix. Determine whether the statement below is true or false. Justify the answer. An eigenspace of A is a null space of a certain matrix. Choose the correct answer below. A. The statement is false. An eigenspace of A is not a null space of a certain matrix because an eigenspace consists of all the eigenvectors corresponding to an eigenvalue 2, and eigenvectors are by definition nonzero vectors, so the eigenspace does not include the zero vector. O B. The statement is false. An eigenspace of A is not a null space of a certain matrix because an eigenspace consists of all solutions x to the equation Ax = Ab, which does not include the zero vector unless b= 0. O C. The statement is true. An eigenspace of A corresponding to the eigenvalue A is the null space of the matrix (A - I). O D. The statement is true. An eigenspace of A corresponding to the eigenvalue A is the null space of the matrix (A - AI).
A is an nxn matrix. Determine whether the statement below is true or false. Justify the answer. An eigenspace of A is a null space of a certain matrix. Choose the correct answer below. A. The statement is false. An eigenspace of A is not a null space of a certain matrix because an eigenspace consists of all the eigenvectors corresponding to an eigenvalue 2, and eigenvectors are by definition nonzero vectors, so the eigenspace does not include the zero vector. O B. The statement is false. An eigenspace of A is not a null space of a certain matrix because an eigenspace consists of all solutions x to the equation Ax = Ab, which does not include the zero vector unless b= 0. O C. The statement is true. An eigenspace of A corresponding to the eigenvalue A is the null space of the matrix (A - I). O D. The statement is true. An eigenspace of A corresponding to the eigenvalue A is the null space of the matrix (A - AI).
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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A is an nxn matrix. Determine whether the statement below is true or false. Justify the answer.
An eigenspace of A is a null space of a certain matrix.
Transcribed Image Text:A is an nxn matrix. Determine whether the statement below is true or false. Justify the answer.
An eigenspace of A is a null space of a certain matrix.
Choose the correct answer below.
A. The statement is false. An eigenspace of A is not a null space of a certain matrix because an eigenspace consists of all the eigenvectors
corresponding to an eigenvalue 2, and eigenvectors are by definition nonzero vectors, so the eigenspace does not include the zero vector.
O B. The statement is false. An eigenspace of A is not a null space of a certain matrix because an eigenspace consists of all solutions x to the
equation Ax = Ab, which does not include the zero vector unless b= 0.
O C. The statement is true. An eigenspace of A corresponding to the eigenvalue A is the null space of the matrix (A - I).
O D. The statement is true. An eigenspace of A corresponding to the eigenvalue A is the null space of the matrix (A - AI).
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