This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Math 33A, Section 3, Fall 2009 Quiz #4 Solutions 1. 23
= 2 · 6 − 3 · 4 = 12 − 12 = 0
46 2. −9 4
= (−9) · 1 − 4 · (−2) = −9 + 8 = −1
−2 1 3. There is only one nonzero pattern, and it has 3 inversions.
002
0 3 0 = −2 · 3 · 5 = −30
500
4. We subtract 2 times row I from row II, and 3 times row I from row III.
111
111
2 3 4 = 0 1 2 =1·1·3=3
336
003
5. We ﬁrst factor out 1 and 1 from rows I and III respectively, and then realize that the
3
5
obtained determinant has two equal rows.
2
3 7
3 5
789 =
27
3
55 1
3 2 7 15
·1· 7 8 9 =0
5
2 7 15 6. If we subtract row I from row III, we get precisely row II.
3
2
5
6 2
3
5
7 4
1
5
8 1
32
4
23
=
5
23
9
67 4
1
1
8 1
4
=0
4
9 7. There is only one nonzero pattern, and it has 6 inversions.
0
0
0
1
0 0
1
0
0
0 0
0
0
0
1 1
0
0
0
0 0
0
1 =1·1·1·1·1·1=1
0
0 1 8. The matrix is lowertriangular.
1
2
3
4
5 0
−1
−2
−3
−4 00
00
10
2 −1
3 −2 0
0
0 = 1 · (−1) · 1 · (−1) · 1 = 1
0
1 9. There is only one nonzero pattern, and it has 5 inversions.
0
8
1
0
0 0
3
0
0
0 5
8
9
4
7 9
6
4
0
1 2
1
3 = −2 · 3 · 1 · 4 · 1 = −24
0
0 10. The matrix is blockuppertriangular and each of the blocks is lowertriangular.
10
5 −2
46
00
00
00 0 5 −7 9
0 8 6 −3
100
300
24 5 7
= 5 −2 0 · 9 1 0 = (1 · (−2) · 2) · (3 · 1 · (−1)) = 12
03 0 0
462
−9 8 −1
09 1 0
0 −9 8 −1 V. K. 2 ...
View
Full
Document
This note was uploaded on 05/29/2011 for the course MATH 33a taught by Professor Lee during the Spring '08 term at UCLA.
 Spring '08
 lee
 Math

Click to edit the document details