Answer Happy

The result of doing these eperations will be to clear the pivot colurn . (Try themt) weme We can (and should!) use sttaller numbers wher the coefficients have a coemon factor, For instance, inctead of using 2R3​+6R2​ as we did in the cecter matris, it is betser to use R3​+3R2​ (divide the original coefficienty 2 and 6 ary the coemmoe factor 2 ) Similarly, 8R3​−12R2​ could be replaced by⋅2R3​−3R2​ (divide by the cotumno factor 4 ). The result of using the smaller coefticients will be a matrix with smaller कtaries. Example for you Write down the row operations aR Rj​R2​ necdod fo clcar the pivot colan. ⎣⎡​76e​3−7a​41E​113​⎦⎤​ Bow te fedoce a Mutris We are now ready to write down the steps needed to coenpletely reduce a matrix iand hence write down the solution of the system of equations it mary repecscall). Step 1: Clear all fractions and or Decimals (if any). We clear fractions and decinals by traltiplying the tows that contain them by euisule integers In the example we are considering, we can do this by multiplying the first twe by 6 and the second row by 4 as follows: [11​−1​21​21​​41​21​​]e4​→∣10​+11​3​] Example of Step 1 for you: Q Enter the row instructions becescary to eliminate fractiots and decimalk, and also apply them.f (For example, to enter the instruction that multiglies Row-1 by 20, fype 20R2. To leave a row alone. leave the instructive blark.) ⎣⎡​−1 क1 e2  w es ​32​−11t​​61​=14​21​⎦⎤​ Step 2: Designate the first nonzero entry in the first row as the pivot and clear its column. Terminology: The first nonzero cmtry in a row is called the leading entry of that ros: Thus, the pivot will be the first element in the first row, unless it is aero, in which cime we would we the first onc that is nonrere in that row. (If the wbols tow is reno, then wit skip this step. In the examnle we are considerine, the nivot is thercfore the i1. 1hentre: