Learning How To Do Row Reduction Takes Practice, and Is an Art!Using Row Reduction – Just as you would if putting in RREF(I.e. By making pivots and using the 1 to make zeros below. Before adding and subtracting multiples of rows, I would put row entries in terms of a common denominatorso that I could do the calculation in my head. When completed, I multiplied the row by the common denominator to return to whole numbers.)43751132111233544375113211124343451441434304242420424246043434514133022202260434345141*41*41*41330222062621043434516*41*4166618306126122062621043434516*41*410624006166160062621043434516*41*4102400161600626210434345161*61*6*41*410240011006262104343451)16(*61*41*41240001100626210434345161=424*61Calculation Involved: Writing ~200 numbers.6 vertical inches of paper space. Very complicated with lots of mental calculations.Lots of fractions!Using Row Reduction – But more efficiently A(I exploit the fact that I do not need a value of 1 in pivot positions and always multiply rather than divide inside the matrix in order to get rows to cancel out.) 4375113211123354437522642224335421*21211122642224335441211111101130335441844411101130335441*41511011101130335441*41=400011101130335441*41400033301130335431*41*41400044001130335431*41*41 4*4*3*4*31*41*41=4Calculation Involved: Writing ~150 numbers.3 vertical inches of paper space. Little mental calculation.No fractions inside the matrix!Using Row Reduction – But more efficiently B(Now I also avoid multiplying. I focus on adding and subtracting rows to make zeros or smaller numbers.)4375113211123354=1021113211123354=1021113211122222=1021113211121110==1021113200021110=1020113000021110=1020011000021110=1020011000021000=0020011000021000=0020010000021000=0200001020000001Calculation Involved: Writing ~150 numbers.3 vertical inches of paper space. Little mental calculation. Fun!Using Row Reduction – But more efficiently C (using column operations)4375113211123354=1375013201120354=1000013201120354=1000013101110351=1000003100110251=1000003100110200=1000002000110200=1000002000010200=1000002000010200=-1000020000010020=+1000020000100002=4Calculation Involved: Writing 160 numbers.2 vertical inches of paper space. Easy and fun!Using Row Reduction – But more efficiently D4375113211123354=1375013201120354=1000013201120354=1000013201120354=1000002001120354=1000002001020304=1000002001010301=1000002002000301=-1000020000200301=4Calculation Involved: Writing 144 numbers.2 vertical inches of paper space. Using Row Reduction – But more efficiently E4375113211123354=1375013201120354C4=C4-C1=1000013201120354Use C4 as a“pivot”.=1000013001100352C1=C1-2C3=1000020001100352 =4R3=R3-3R2Calculation Involved: Writing 80 numbers.1 vertical inch of paper space. Easy and