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2 RREF (4 points) Next, you will use these tow operations to write a function that performs Gauss. Jordan elimination and compute the reduced row echelon form of any matrix We will call the function my rref, because the Tref function already exists in MATLAB Specification: function R - my_rref(A) Input: a rectangular matrix A. Output: the reduced row echelon form of A For full credit your function should handle the following: Partial proting: At each step, you should swap the current row with the one whose entry in the pivot column has the largest absolute value Free triables: Due to numerical error, the entries in a column corre ponding to a free variable may be extremely small but not precisely were Therefore, you should consider an entry to be zero if its alveolute value is smaller than 10-12 We suggest first implementing the algorithm without considering these two i then adding code to deal with them one at a time. Implementation tips: There are two different ways one can implement Jordan elimination. . In Section 1.2 under "The Row Reduction Algorithm", the book describes it in two phases: first do Gaussian elimination (Steps 1-4), then perform TOW operations equivalent to back-substitution (Step 5). Gan Jordan elimination can also be done in a single phw every time you find a pivot, perform scaling so the pirat entry becomes 1, then perform elimination on all the other rows, both a re and below the pivot now You may use either approach in your implementation. Below, we provide pseudocode for the latter approach In either cas, since we want to be 0 . 0 able to handle free variables, the pivot . . . 10 . O . entry won't necessarily be on the di- 0 0 0 - - - - agonal Instead, you'll need to keep 0 0 0 O N . . track of hoth the pivot row, wyk, and the pivot column, l, as you go along 0 0 0 0 - - - - 00.- the illustration on the right entry is com Algorithm RRET 1 initimli pivot uw 1, pivot column while ISA ISIS n do grow to find the row with the RR is be the + 1 ne R (1 ) , for i 1.. - +.. do | R R (4 4 4 I. end for El 16 end while