Matrix Inverse Issue

• To: mathgroup at smc.vnet.net
• Subject: [mg80556] Matrix Inverse Issue
• From: "Brian Gladman" <brg at nowhere.org>
• Date: Sun, 26 Aug 2007 03:00:40 -0400 (EDT)

```I am having a problem with the matrix inverse for the following matrix in
Mathematica 6:

A = Table[If[j == i, 1 - i/10, If[j == i + 1, i/10, 0]], {i, 9}, {j, 9}]

{{9/10, 1/10, 0, 0, 0, 0, 0, 0, 0}, {0, 4/5, 1/5, 0, 0, 0, 0, 0,
0}, {0, 0, 7/10, 3/10, 0, 0, 0, 0, 0}, {0, 0, 0, 3/5, 2/5, 0, 0, 0,
0}, {0, 0, 0, 0, 1/2, 1/2, 0, 0, 0}, {0, 0, 0, 0, 0, 2/5, 3/5, 0,
0}, {0, 0, 0, 0, 0, 0, 3/10, 7/10, 0}, {0, 0, 0, 0, 0, 0, 0, 1/5, 4/
5}, {0, 0, 0, 0, 0, 0, 0, 0, 1/10}}

A Inverse[A]

{{1, -1/72, 0, 0, 0, 0, 0, 0, 0}, {0, 1, -1/14, 0, 0, 0, 0, 0, 0}, {0,
0, 1, -3/14, 0, 0, 0, 0, 0}, {0, 0, 0, 1, -8/15, 0, 0, 0, 0}, {0,
0, 0, 0, 1, -5/4, 0, 0, 0}, {0, 0, 0, 0, 0, 1, -3, 0, 0}, {0, 0, 0,
0, 0, 0, 1, -49/6, 0}, {0, 0, 0, 0, 0, 0, 0, 1, -32}, {0, 0, 0, 0,
0, 0, 0, 0, 1}}

I expected the identity matrix here but I get extra terms.

Am I doing something wrong?