A is an nxn matrix. Determine whether the statement below is true or false. Justify the answer. The eigenvalues of a matrix are on its main diagonal. Choose the correct answer below. O A. The statement is true. The eigenvalues of a matrix are on its main diagonal because the main diagonal determines the pivots of the matrix, which are used to calculate the eigenvalues. O B. The statement is true. The eigenvalues of a matrix are on its main diagonal because the main diagonal remains the same when the matrix is transposed, and a matrix and its transpose have the same eigenvalues. Oc. The statement is false. If the matrix is a triangular matrix, the values on the main diagonal are eigenvalues. Otherwise, the main diagonal may or may not contain eigenvalues. O D. The statement is false. The matrix must first be reduced to echelon form. The eigenvalues are on the main diagonal of the echelon form of the matrix.
A is an nxn matrix. Determine whether the statement below is true or false. Justify the answer. The eigenvalues of a matrix are on its main diagonal. Choose the correct answer below. O A. The statement is true. The eigenvalues of a matrix are on its main diagonal because the main diagonal determines the pivots of the matrix, which are used to calculate the eigenvalues. O B. The statement is true. The eigenvalues of a matrix are on its main diagonal because the main diagonal remains the same when the matrix is transposed, and a matrix and its transpose have the same eigenvalues. Oc. The statement is false. If the matrix is a triangular matrix, the values on the main diagonal are eigenvalues. Otherwise, the main diagonal may or may not contain eigenvalues. O D. The statement is false. The matrix must first be reduced to echelon form. The eigenvalues are on the main diagonal of the echelon form of the matrix.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.8: Determinants
Problem 38E
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A is an nxn matrix. Determine whether the statement below is true or false. Justify the answer.
The eigenvalues of a matrix are on its main diagonal.
![A is an nxn matrix. Determine whether the statement below is true or false. Justify the answer.
The eigenvalues of a matrix are on its main diagonal.
Choose the correct answer below.
O A. The statement is true. The eigenvalues of a matrix are on its main diagonal because the main diagonal determines the pivots of the matrix,
which are used to calculate the eigenvalues.
O B. The statement is true. The eigenvalues of a matrix are on its main diagonal because the main diagonal remains the same when the matrix is
transposed, and a matrix and its transpose have the same eigenvalues.
Oc. The statement is false. If the matrix is a triangular matrix, the values on the main diagonal are eigenvalues. Otherwise, the main diagonal may
or may not contain eigenvalues.
O D. The statement is false. The matrix must first be reduced to echelon form. The eigenvalues are on the main diagonal of the echelon form of the
matrix.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F94526f5d-1fce-4c5f-914f-b8b3722c8f68%2F196a56ea-d71c-4ff8-9492-e9ea2d7d9845%2Fwp7iwh_processed.png&w=3840&q=75)
Transcribed Image Text:A is an nxn matrix. Determine whether the statement below is true or false. Justify the answer.
The eigenvalues of a matrix are on its main diagonal.
Choose the correct answer below.
O A. The statement is true. The eigenvalues of a matrix are on its main diagonal because the main diagonal determines the pivots of the matrix,
which are used to calculate the eigenvalues.
O B. The statement is true. The eigenvalues of a matrix are on its main diagonal because the main diagonal remains the same when the matrix is
transposed, and a matrix and its transpose have the same eigenvalues.
Oc. The statement is false. If the matrix is a triangular matrix, the values on the main diagonal are eigenvalues. Otherwise, the main diagonal may
or may not contain eigenvalues.
O D. The statement is false. The matrix must first be reduced to echelon form. The eigenvalues are on the main diagonal of the echelon form of the
matrix.
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