(1 point) Diagonalization Enter T or F depending on whether the statement is tru
ID: 3282746 • Letter: #
Question
(1 point) Diagonalization Enter T or F depending on whether the statement is true or false. (You must enter T or F -- True and False will not work.) Assume that all matrices in the following statements are square. 1. If P-1AP is a diagonal matrix, then the columns of P are eigenvectors of A. 2. If the matrix A has an eigenvalue whose algebraic multiplicity in the characteristic polynomial of A is greater than one, then A is not diagonalizable. 3. A matrix which is not invertible is not diagonalizable. 4. The matrix [ 0 ] is not diagonalizable. 5. If A is diagonalizable, then there exists a unique invertible matrix P such that P ' AP is diagonal.Explanation / Answer
1- T
2-F it may or may not be diagonal depends on am = gm
3-F [0 0;0 1] is not invertible but diagonal
4-T nilpotent matrix is diagonal if and only if it is zero matrix.
5-F eigen vectors are not unique.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.