A set of linear equations is given in the form $Ax=b$, where A is a $2\times 4$ matrix with real number entries and $b\neq 0.$ will it be possible to solve for $x$ and obtain a unique solution by multiplying both left and right sides of the equation by $A^T$ (the super script $T$ denotes the transpose) and inverting the matrix $A^TA?$ Answer is _________
- Yes, it is always possible to get a unique solution for any $2\times 4$ matrix A.
- No, it is not possible to get a unique solution for any $2\times 4$ matrix A.
- Yes, can obtain a unique solution provided the matrix $A^T A$ is well conditioned
- Yes, can obtain a unique solution provided the matrix $A$ is well conditioned