Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. The determinant of a triangular matrix is the sum of the entries on the main diagonal. Choose the correct answer below. O A. The statement is true. Cofactor expansion along the row (or column) with the most zeros of a triangular matrix produces a determinant equal to the sum of the entries along the main diagonal. O B. The statement is true. The determinant of A is the following finite series. det A = E(-1)' *laydet Aj j= 1 In a triangular matrix, this series simplifies to the sum of the entries along the main diagonal. O c. The statement is false. The determinant of a triangular matrix is the product of the entries along the main diagonal. O D. The statement is false. The determinant of a matrix is the arithmetic mean of the entries along the main diagonal.
Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer. The determinant of a triangular matrix is the sum of the entries on the main diagonal. Choose the correct answer below. O A. The statement is true. Cofactor expansion along the row (or column) with the most zeros of a triangular matrix produces a determinant equal to the sum of the entries along the main diagonal. O B. The statement is true. The determinant of A is the following finite series. det A = E(-1)' *laydet Aj j= 1 In a triangular matrix, this series simplifies to the sum of the entries along the main diagonal. O c. The statement is false. The determinant of a triangular matrix is the product of the entries along the main diagonal. O D. The statement is false. The determinant of a matrix is the arithmetic mean of the entries along the main diagonal.
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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Let A be an n x n matrix. Determine whether the statement below is true or false. Justify the answer.
The determinant of a triangular matrix is the sum of the entries on the main diagonal.
Transcribed Image Text:Let A be an nxn matrix. Determine whether the statement below is true or false. Justify the answer.
The determinant of a triangular matrix is the sum of the entries on the main diagonal.
Choose the correct answer below.
O A. The statement is true. Cofactor expansion along the row (or column) with the most zeros of a triangular matrix produces a determinant equal to
the sum of the entries along the main diagonal.
O B. The statement is true. The determinant of A is the following finite series.
n
det A = E(-1)'*la
4jdet A1j
j= 1
In a triangular matrix, this series simplifies to the sum of the entries along the main diagonal.
O c. The statement is false. The determinant of a triangular matrix is the product of the entries along the main diagonal.
O D. The statement is false. The determinant of a matrix is the arithmetic mean of the entries along the main diagonal.
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