Row-reduce [ 270 51 70 | 400 ] 10 5.4 15 | 30 2 5.2 0 | 10 I have a general understanding, but the big numbers are throwing me off

What son of a feather gave you this problem? Well you can multiply the second row by 27 and subtract the first row from the second. That would make the first entry of the second row 0, the second entry 5.4*27 - 51 = 94.8, the third entry 15*27 - 70 = 335, fourth entry 30*27-400 = 410. Then you can multiply the third row by 135 and subtract the first row, which would make the first entry of the last row 0; second entry 5.2*135 - 51 = 651; third entry -70; fourth entry 1350-400 = 950. And so on.

okei as i see this is just a simple gauss elimination , just forget the augmented part for a while and make (1,1) zero, then look forward to make (1'2) zero n so on... it's just a simple problem given to you, which just needs only calculation skills

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