Re: Possible Bug in Mathematica 6

• To: mathgroup at smc.vnet.net
• Subject: [mg90240] Re: [mg90184] Possible Bug in Mathematica 6
• From: DrMajorBob <drmajorbob at att.net>
• Date: Thu, 3 Jul 2008 06:10:55 -0400 (EDT)
• References: <19823722.1215015456847.JavaMail.root@m08>

```I'm curious how you used Det on a 6-by-9 (non-square) matrix:

m = {{f_ 11, f_ 12, f_ 13, 0, 0, 0, 0, 0, 0}, {0, 0, 0, f_ 21, f_ 22,
f_ 23, 0, 0, 0}, {0, 0, 0, 0, 0,
0, (a f_ 11 + b f_ 21), (a f_ 12 + b f_ 22), (a f_ 13 +
b f_ 23)}, {f_ 21, f_ 22, f_ 23, f_ 11, f_ 12, f_ 13, 0, 0,
0}, {(a f_ 11 + b f_ 21), (a f_ 12 + b f_ 22), (a f_ 13 +
b f_ 23), 0, 0, 0, f_ 11, f_ 12, f_ 13}, {0, 0,
0, (a f_ 11 + b f_ 21), (a f_ 12 + b f_ 22), (a f_ 13 + b f_ 23),
f_ 21, f_ 22, f_ 23}};

Dimensions@m

{6, 9}

RowReduce@m

{{1, 0, -1, 0, 0, 0, 0, 12/(11 a + 21 b), 24/(11 a + 21 b)}, {0, 1, 2,
0, 0, 0, 0, -(11/(11 a + 21 b)), -(22/(11 a + 21 b))}, {0, 0, 0, 1,
0, -1, 0, 22/(11 a + 21 b), 44/(11 a + 21 b)}, {0, 0, 0, 0, 1, 2,
0, -(21/(11 a + 21 b)), -(42/(11 a + 21 b))}, {0, 0, 0, 0, 0, 0,
1, (2 (6 a + 11 b))/(11 a + 21 b), (13 a + 23 b)/(11 a + 21 b)}, {0,
0, 0, 0, 0, 0, 0, 0, 0}}

(5 independent rows.)

RowReduce@Transpose@m

{{1, 0, 0, 0, 0, a^2/b}, {0, 1, 0, 0, 0, b}, {0, 0, 1, 0, 0, 1/b}, {0,
0, 0, 1, 0, a}, {0, 0, 0, 0, 1, -(a/b)}, {0, 0, 0, 0, 0, 0}, {0, 0,
0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0}}

(5 independent columns.)

MatrixRank@m

5

(Rank 5.)

I don't see a problem.

Bobby

On Tue, 01 Jul 2008 06:02:57 -0500, Amir Ahmed Ansari
<aansari at softpak.com> wrote:

> Hi,
>
> I tried this on a friend=92s computer using Mathematica 6. Consider the
> following matrix:
>
> {
>     { f_11, f_12, f_13, 0, 0, 0, 0, 0, 0 },
>     { 0, 0, 0, f_21, f_22, f_23, 0, 0, 0 },
>     { 0, 0, 0, 0, 0, 0, ( a f_11 + b f_21 ), ( a f_12 + b f_22 ), =
> ( a f_13 +
> b f_23 ) },
>     { f_21, f_22, f_23, f_11, f_12, f_13, 0, 0, 0 },
>     { ( a f_11 + b f_21 ), ( a f_12 + b f_22 ), ( a f_13 + b f_23 =
> ), 0, 0,
> 0, f_11, f_12, f_13 },
>     { 0, 0, 0, ( a f_11 + b f_21 ), ( a f_12 + b f_22 ), ( a f_13 =
> + b f_23
> ), f_21, f_22, f_23 }
> }
>
>
> All 5x5 have a determinant of 0 as can be seen by using Det[]. Yet,
> MatrixRank[] comes out to be 5. Is this a bug or am I doing something
> stupid?
>
>
>
>

--
DrMajorBob at longhorns.com

```

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