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Possible Bug in Mathematica 6

• To: mathgroup at smc.vnet.net
• Subject: [mg90184] Possible Bug in Mathematica 6
• From: "Amir Ahmed Ansari" <aansari at softpak.com>
• Date: Tue, 1 Jul 2008 07:02:57 -0400 (EDT)

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?