True or False? In Exercises 69 and 70, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text.
(a) An eigenvalue of a matrix A is a scalar
(b) An eigenvector may be the zero
(c) A matrix A is orthogonally diagonalizable when there exists an orthogonal matrix P such that
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Elementary Linear Algebra (MindTap Course List)
- CAPSTONE Explain how to determine whether an nn matrix A is diagonalizable using a similar matrices, b eigenvectors, and c distinct eigenvalues.arrow_forwardFill in the blanks. To encode a message, create an invertible matrix A and multiply the row matrices by A (on the right) to obtain the row matrices.arrow_forwardTrue or False? In Exercises 67 and 68, determine whether each statement is true or false. If a statement is true, give a reason or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. a Geometrically, if is an eigenvalue of a matrix A and x is an eigenvector of A corresponding to , then multiplying x by A produce a vector x parallel to x. b If A is nn matrix with an eigenvalue , then the set of all eigenvectors of is a subspace of Rn.arrow_forward
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