I want to ask, if rank of matrix with right side (Ab=3), is greater than the rank of the matrix without it (A=2) does it mean that matrix does not have solution?
Thanks
2026-03-26 22:13:46.1774563226
Rank of the matrices
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Yes, to determine whether there are no solutions, a unique solution or infinite many solutions, use the following conditions :
$1)$ The matrix $A$ and the matrix emerging by concatenating $A$ and $b$ must have the same rank. If this is not the case, there is no solution. If it is the case, then continue with $2)$
$2)$ If the rank of the matrix $A$ is equal to the number of unknowns, the solution is unique, otherwise there are infinite many solutions.