Quick easy question about Row echelon form

[dalarev]

So google has yielded no good results. When I "transform" a matrix to row echelon form, not reduced row echelon form (leading entries are not necessarily 1), what does it mean if my last row is all 0's? Another thing, when setting up the equations as a matrix, do I include the solutions of the equations in there?
I did them with Cramer's rule and did not need the solution in the matrix. Thanks for the help.

 

[HallsofIvy]

It means that the rank of your matrix is one less than the dimension of the matrix. It also means that a system of equations having that matrix as coefficient matrix will not have a unique solution- either no solution or an infinite number of solutions.

Whether you include the "solutions of the equations" (by which I think you mean the right-hand side of the equations: the numbers not multiplying a variable- surely you do not mean the "solutions" to the equations!) depends on what you want to do with the matrix!

One way of solving a matrix equation, or system of equations converted to matrix form, is to find the inverse of the matrix multiplying the "unknown" vector and multiply both sides of the equation by it. In that case the matrix must include only the coefficients.

But I suspect you are talking about using row reduction. In that case, in order to apply the same row operations to the "right-hand side", you form the "augmented matrix", including the right-hand side as an additional column.

 

[dalarev]

It means that the rank of your matrix is one less than the dimension of the matrix. It also means that a system of equations having that matrix as coefficient matrix will not have a unique solution- either no solution or an infinite number of solutions.

Whether you include the "solutions of the equations" (by which I think you mean the right-hand side of the equations: the numbers not multiplying a variable- surely you do not mean the "solutions" to the equations!) depends on what you want to do with the matrix!

One way of solving a matrix equation, or system of equations converted to matrix form, is to find the inverse of the matrix multiplying the "unknown" vector and multiply both sides of the equation by it. In that case the matrix must include only the coefficients.

But I suspect you are talking about using row reduction. In that case, in order to apply the same row operations to the "right-hand side", you form the "augmented matrix", including the right-hand side as an additional column.

exactly what I was asking. Thanks a bunch.