710 4107 10-1 0414 (d)

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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Please answer D
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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