Matrix with No InverseDate: 06/13/2005 at 09:55:27 From: Saul Subject: Solving 3x3 matrix Are there any 3x3 matrices that do not have inverses and if so, where do I find them? Date: 06/13/2005 at 14:31:17 From: Doctor Samuel Subject: Re: Solving 3x3 matrix Hi Saul, A matrix has an inverse if and only if its determinant is nonzero. Thus, for a 3x3 matrix A, [ a1 a2 a3 ] A = [ b1 b2 b3 ] [ c1 c2 c3 ] The inverse of A doesn't exist iff a1*b2*c3 + a2*b3*c1 + a3*b1*c2 - a1*b3*c2 - a3*b2*c1 - a2*b1*c3 = 0. From this we can see that A cannot have an inverse if, for example, a1 = a2 = a3 = 0. Matrices that don't have inverses are called "singular". Perhaps you can find other values for which A is singular? Hope this helps. Please write back if you are still stuck. - Doctor Samuel, The Math Forum http://mathforum.org/dr.math/ |
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