Problem7 testcase4 bugfix

[bigfoot1144]

Problem

Where the equation does not need S to be invertible. Which causes further confusion in the "learn about this topic" page. Where they only check for invertibility of T because that's the only place its necessary to solve the equation.

solution

• Remove check for invertibility of S
• change problem 4 edge case to make T determinant 0.
• Also change verbiage of the problem to reflect that only T needs invertibility check. (Not possible through PR I think?)

[BjBodner]

Hi, totally agree with your assessment in the context of the minimal requirements for this code to run. However, since A can be full rank, if S is not invertible, this means that this transformation will reduce the rank of the resulting matrix, making it IRREVERSIBLE.
Usually, such transformations are required to be REVERSIBLE, which can only happen if BOTH S and T are invertible. This is kinda similar to applying a rotation matrix to a vector, however, here we are "rotating" a matrix.

Perhaps it would be worth mentioning this in the description of the question, that this is what we are trying to do: "apply a REVERSIBLE transformation to A", since in the current formulation it is not clear, and then your proposal totally makes sense.