The problem is to solve an equation of 5 variables with 5 equations. Making it into a matrix the left side looks like an identity matrix. The first time I solved this I did it long hand – which took forever – then I took another look and saw what they person framing the problem was thinking. Which is cool since this trick should make it easier to attack matrix reduction for some annoying cases.
Sum all of the rows to create the new vector S. Then since all the columns of S have the same value it can be normalized so all the values of S are unity. Then by subtracting S from each of the rows (a..e) we create a new matrix M. Multiply M by negative 1 to keep the values at unit as opposed to negative unity and the solution is done. Most important it is done without the page of long hand reduction.
