Hello - i started working on this problem and wanted some help with it:

Findfor which the system will have only one solution:a

http://img805.imageshack.us/img805/9...reenshotla.png

tnx in advance

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- May 4th 2011, 02:16 PMkaragorgeLinear system equation problem
Hello - i started working on this problem and wanted some help with it:

Findfor which the system will have only one solution:**a**

http://img805.imageshack.us/img805/9...reenshotla.png

tnx in advance - May 4th 2011, 02:30 PMTinyboss
It's either every choice of a, or no choice of a. Convert this into a matrix-vector equation Ax=b(a). I write b(a) to denote a vector b that depends on the choice of a. Then you're asking for values of a such that the preimage of b(a) under the linear transformation A is a single vector. But that happens (no matter what b(a) is) if and only if A is injective, i.e. when the matrix A is non-singular. If A is singular (zero determinant), then you may have no solution or infinitely many solutions, depending on a, but never a unique solution.