Problem I Determine for which values of the real parameter a the following matrix is not invertible. 5. 9. 13. 17. a 1 1 α) 1 01 1 01 D 1 1 011 01 1 10 ιιια 0 a 1 1 1 10 1 1 1a 01 a 1 101 1 01 6. 10. 14. 18. 0 1 1 1 a 0 1 a 101 1 1 0, 1 1 1 11 αι 110 1 1 1 1 0 a 1 a 0 1 10 D 1110 0 0, 1 11 1011 a 110, 0 1 1 1 101 a 1101 10 D 3. 7. 11. 15. 19. 0 1 1 1 1011 α 1 1 1 10, a 1 1 1 1011 11 1 I 0, D 1 101 1 110 a 1 0 0 1 0 1 a 1 10 11 1 1 a 1 1 1 0 III 0, € 01 1 1101 1 a 0 | 4. 12. 16. 20. I 0/ a 0 1 10 1 a 01 1 01 D 1 0, a a 101 1 101 0 D 10 11 a 10 1 0 0 a 11 1011 1 1 0 a
Problem I Determine for which values of the real parameter a the following matrix is not invertible. 5. 9. 13. 17. a 1 1 α) 1 01 1 01 D 1 1 011 01 1 10 ιιια 0 a 1 1 1 10 1 1 1a 01 a 1 101 1 01 6. 10. 14. 18. 0 1 1 1 a 0 1 a 101 1 1 0, 1 1 1 11 αι 110 1 1 1 1 0 a 1 a 0 1 10 D 1110 0 0, 1 11 1011 a 110, 0 1 1 1 101 a 1101 10 D 3. 7. 11. 15. 19. 0 1 1 1 1011 α 1 1 1 10, a 1 1 1 1011 11 1 I 0, D 1 101 1 110 a 1 0 0 1 0 1 a 1 10 11 1 1 a 1 1 1 0 III 0, € 01 1 1101 1 a 0 | 4. 12. 16. 20. I 0/ a 0 1 10 1 a 01 1 01 D 1 0, a a 101 1 101 0 D 10 11 a 10 1 0 0 a 11 1011 1 1 0 a
Problem I Determine for which values of the real parameter a the following matrix is not invertible. 5. 9. 13. 17. a 1 1 α) 1 01 1 01 D 1 1 011 01 1 10 ιιια 0 a 1 1 1 10 1 1 1a 01 a 1 101 1 01 6. 10. 14. 18. 0 1 1 1 a 0 1 a 101 1 1 0, 1 1 1 11 αι 110 1 1 1 1 0 a 1 a 0 1 10 D 1110 0 0, 1 11 1011 a 110, 0 1 1 1 101 a 1101 10 D 3. 7. 11. 15. 19. 0 1 1 1 1011 α 1 1 1 10, a 1 1 1 1011 11 1 I 0, D 1 101 1 110 a 1 0 0 1 0 1 a 1 10 11 1 1 a 1 1 1 0 III 0, € 01 1 1101 1 a 0 | 4. 12. 16. 20. I 0/ a 0 1 10 1 a 01 1 01 D 1 0, a a 101 1 101 0 D 10 11 a 10 1 0 0 a 11 1011 1 1 0 a
Transcribed Image Text:Problem I Determine for which values of the real parameter a the following matrix is not
invertible.
1.
5.
9.
13.
17.
a 11 a
101 1
1 1 0 1
1110
a 1 1 1
101 1
1
a
0 a
1
a 0 1 1
1 0 1
1 1 0
10
1 1 1
1
1
1 1 1
1011
a
1 a 01
1 1 10
0 1 a 1
10 1 1
a 10 1
1
1 1 0
2.
6.
10.
14.
18.
0 1 1 1
0
1 a
01
10
0 1 1
1
1
1
1
0
0 1 1
1
10 a 1
1 a0 1
10
a
1 1
01 1
a
1
10
1 1
1 a
01
1 0
3.
7.
11.
15.
19.
0 1 1 1
101 1
a 1 0 a
11 0
1 1 1
0 1 1
a 1
0
1 1 1
011
1 10 a
1 a 0
0 1 a 1
101 1
10 a
110
0
1 1
1
a 0 1 1
10 1
1 1 a 0
4.
8.
12.
16.
20.
0 1 1 1
1 0 1 1
10 1
1
a
0 1 1 1
1
a
a
1
1
a
1
0 1
10
1 101
a 1 10
01
1 0 1
a
1
a
1
a 10 1
1 1 0
0 a
10 11
1 10
a
1 1 0
Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.
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