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8. Let A be a square matrix of order n > 3, and suppose that det(A) = 3. Find the following determinants (a) det(A₁), where A₁ is obtained from A by switching the third row and the first row; (b) det(A₂), where A2 is obtained from A by adding 3 times the first row to the last row, ther multiply the new last row by -2; (c) * det(A3), where A3 is obtained from A by rearranging the rows of A so that the first row becomes the last row and the rest of rows get shifted upward by one row.

8. Let A be a square matrix of order n > 3, and suppose that det(A) = 3. Find the following determinants (a) det(A₁), where A₁ is obtained from A by switching the third row and the first row; (b) det(A₂), where A2 is obtained from A by adding 3 times the first row to the last row, ther multiply the new last row by -2; (c) * det(A3), where A3 is obtained from A by rearranging the rows of A so that the first row becomes the last row and the rest of rows get shifted upward by one row.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.2: Direct Methods For Solving Linear Systems
Problem 22EQ: Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be...
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8. Let A be a square matrix of order n > 3, and suppose that det(A) = 3. Find the following determinants (a) det(A₁), where A₁ is obtained from A by switching the third row and the first row; (b) det(A₂), where A2 is obtained from A by adding 3 times the first row to the last row, then multiply the new last row by -2; (c) * det(A3), where A3 is obtained from A by rearranging the rows of A so that the first row becomes the last row and the rest of rows get shifted upward by one row.
Transcribed Image Text:8. Let A be a square matrix of order n > 3, and suppose that det(A) = 3. Find the following determinants (a) det(A₁), where A₁ is obtained from A by switching the third row and the first row; (b) det(A₂), where A2 is obtained from A by adding 3 times the first row to the last row, then multiply the new last row by -2; (c) * det(A3), where A3 is obtained from A by rearranging the rows of A so that the first row becomes the last row and the rest of rows get shifted upward by one row.
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