2. Verify that det(AB) = det(A)det(B) forthe following: -2 3 [1 0 2] a) A=-2 3 1 B= 3 -2 5| 1 2 1 3 Г2 3 [3 0 b) A= 0 3 2 B= 4 5 0 0 0 -4 2 1 -2 а 1 B b a 3. Show that = (b- a)(c- a)(b- c). This deteminant is called C Vandermonde determinant.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.2: Determinants
Problem 19EQ
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answer the ff. 2 and 3

2. Verify that det(AB) = det(A)det(B) for the following:
-2 31
1
[1 0 2]
а) А-D —2 3
1
В- 3 -2 5
1
2
1
3
Г2 3
6.
[3 0 0
b) A= 0 3 2
B= 4 5
0 0 -4
2 1 -2
a
a
3. Show that
B b
- (b-а)(с-а)(b- с).
This determinant is called
Vandermonde determinant.
Transcribed Image Text:2. Verify that det(AB) = det(A)det(B) for the following: -2 31 1 [1 0 2] а) А-D —2 3 1 В- 3 -2 5 1 2 1 3 Г2 3 6. [3 0 0 b) A= 0 3 2 B= 4 5 0 0 -4 2 1 -2 a a 3. Show that B b - (b-а)(с-а)(b- с). This determinant is called Vandermonde determinant.
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