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710 4107 10-1 0414 (d)

710 4107 10-1 0414 (d)

Advanced Engineering Mathematics
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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Desired Properties of the Determinant. Let A and B be (n_n)-matrices. P1: If B is obtained from A by interchanging two rows, then det (B) det (A). P2: If B is obtained from A by multiplying one row by k then det (B) = k det(A). P3: If B is obtained from A by adding a multiple of one row to another row (leaving the rst row unchanged), then det(B) = det(A). P4: If A is an upper (or lower) triangular matrix, then det(A)= a₁1ª22 ann.
Transcribed Image Text:Desired Properties of the Determinant. Let A and B be (n_n)-matrices. P1: If B is obtained from A by interchanging two rows, then det (B) det (A). P2: If B is obtained from A by multiplying one row by k then det (B) = k det(A). P3: If B is obtained from A by adding a multiple of one row to another row (leaving the rst row unchanged), then det(B) = det(A). P4: If A is an upper (or lower) triangular matrix, then det(A)= a₁1ª22 ann.
1. Use properties P1-P4 to nd the determinants of the following matrices: 3 1 -1 5 2 1 2 (a) 25 3 (c) 1 3 −1 2 دن مه من 7 13 -1 0 4 1 2 4 1 3 2 -2 -2 2 (b) (d) 0 −1 1 3 2 THO 1 1 0 −1 1 Solution -1 1 1 -1 0 1 0
Transcribed Image Text:1. Use properties P1-P4 to nd the determinants of the following matrices: 3 1 -1 5 2 1 2 (a) 25 3 (c) 1 3 −1 2 دن مه من 7 13 -1 0 4 1 2 4 1 3 2 -2 -2 2 (b) (d) 0 −1 1 3 2 THO 1 1 0 −1 1 Solution -1 1 1 -1 0 1 0
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