Forward elimination changes 1 1 1 2 x = b to a triangular 1 1 0 1 x = c: x + y = 5 x +
Chapter 1, Problem 1.5.20(choose chapter or problem)
Forward elimination changes 1 1 1 2 x = b to a triangular 1 1 0 1 x = c: x + y = 5 x + 2y = 7 x + y = 5 y = 2 " 1 1 5 1 2 7 # " 1 1 5 0 1 2 # . That step subtracted `21 = times row 1 from row 2. The reverse step adds `21 times row 1 to row 2. The matrix for that reverse step is L = . Multiply this L times the triangular system 1 1 0 1 x = 5 2 to get = . In letters, L multiplies Ux = c to give .
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