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.
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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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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