Quick and probably daft matrix question Watch

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loismustdie
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Report Thread starter 14 years ago
#1
just wanted to know, how can you tell if the equation

Ax = b has a unique solution, where A is a matrix and x,b vectors?

Thanks.
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jpowell
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#2
Report 14 years ago
#2
iff the determinant is non zero.
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RichE
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(Original post by loismustdie)
just wanted to know, how can you tell if the equation

Ax = b has a unique solution, where A is a matrix and x,b vectors?

Thanks.
If A is square, then it will have a unique solution if and only if A is invertible (in which case this is the same as having non-zero determinant).

More generally, if you take the augmented matrix (A|b) and row-reduce it then you should get (possibly with some zero rows) (I|c), where I is the identity matrix and c is the solution.
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loismustdie
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Report Thread starter 14 years ago
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thanks
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