Department of Mathemati s, Mahidol University Kit Tyabandha, PhD Examples for linear algebra th 17 January, 2006 1. Solve using the Gaussian elimination, 3x1+8x2 =53 6x1+2x2 =50 Solution. Write the equations in an augmented matrix, (cid:20) (cid:21) 3 8 53 [A B℄= 6 2 50 1 Row 1 times , 3 (cid:20) (cid:21) 8 53 1 3 3 6 2 50 Row 1 subtra ted by 2 times of Row 1, (cid:20) (cid:21) 8 53 1 3 3 0 (cid:0)14 (cid:0)56 1 Row 2 times (cid:0) , 14 (cid:20) (cid:21) 8 53 1 3 3 0 1 4 8 Row 1 subtra ted by times of Row 2, 3 (cid:20) (cid:21) 1 0 7 0 1 4 Therefore x(cid:22)1 =7 and x(cid:22)2 =4. # th Business Mathemati s, Examples for Linear algebra{1{From 17 Jan 06, as of 17 January, 2006