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Questions for Math-1: A course for Biology and Applied Geology students

Abhay Soman

Section A.1 Row reduced echelon form and a system of linear equations

We use online computer algebra system SageMath 1  to compute the row reduced echelon form of a given matrix. In the following example A=matrix(RR,[[1,2,1,-1],[9,7,5,5],[1,-2,2,8]]) represents \(3\times 4\) matrix \(A\) over \(\R\text{.}\) The entries [1,2,1,-1], [9,7,5,5], and [1,-2,2,8] represents the first, the second, and the third row of \(A\text{,}\) respectively.
You may input the matrix of your choice to get the row reduced echelon form. Please first do the calculations yourself and then verify using SageMath.
In the following SageMath can compute the solution of the system \(AX=Y\text{.}\) You may change \(A\) and \(Y\) appropriately.
In the following we can reduced the augmented matrix \([A|v]\) to the row reduced echelon form. You may change \(A\) and \(v\) appropriately.
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