http://www.ck12.org Chapter 8. Systems and Matrices
7.
−1 3 − 4
4 2 1
1 2 5
8.
4 5 8
9 0 1
0 3 − 2
9.
0 7 − 1
2 − 3 1
6 8 0
10.
4 2 − 3
2 4 5
1 8 0
11.
− 2 − 6 − 12
− 1 − 5 − 2
2 3 4
12.
−2 6 3
2 4 0
−8 2 1
- Show that Helmert’s 2×2 matrix is its own inverse:
√^1
2
√^1
1 2
√ 2 −√^12
- Show that Helmert’s 3×3 matrix is its own inverse:
√^1
3
√^1
3
√^1
1 3
√ 2 −√^120
√^1
6
√^1
6 −
√^2
6
.
- Non-square matrices sometimes have left inverses, whereA−^1 ·A=I, or right inverses, whereA·A−^1 =I. Why
can’t non-square matrices have “regular” inverses?