Question

numerical methods question. please explain/solve clearly that is understandable. will give thumbs up if solved in 30 mins correctly

Find the LU decomposition of the matrix. 25 5 4 10 8 16 8 12 22

Answer 1

let 5 25 Ang 4 2. 16 10 8. 12 22 To finding LU - decomposition findo very easy to For that take ALU ; where L is lower a triangular matrix with diagonal element unity an opper as U is and matrix triangular ie uu 412 La اور Uz -- 0 U13 U23 U33 U 22 So, we just have to find this values ALU or uz 125 U12 한 10 5 4 8 16 12 22 le Uu L lgi uu 6 lg + Ugg 131 412 + lzz 422 6 4,37423 + 222 423 be 93 U33 + ملین Nas, compare both side co-efficient, Jug = 4 Jet 4,= 25 [112=5 10 lar. 41 =10 lel lar 2 25

8 K, Ч У А) 2 = 25 - 2 Э ч, 19,9 = y - ua : -1,, ,, 22 - - 16х5 25 Чэр = 6 ДЧ, «Х, Ч, 2 = 12 = 12 ), , , la 29. р 1 12 - 2х5 12 а) , , 25 4 a 52 бо-у 7. 10 А. 1) По я 16 18. 10 х 4 25 36 о 25 2 у T,, Ч, у 1921 u, alr - 1, Ч, 2 Г., у 2 ч. – Чо 2. Чg 1 2 Ч. Чу з 22 2) Муу з 22 - 3,, ,, - ,,ч, а 29 - УЧ - 52 у 12 30 25 36 624 556 - 12 - 24 а 22 - 32. 25 25 я

Ugg 25 L and into U Now, all but Jet 25 5 4 25 5 6 4 360 25 106 25 8 16 22 25 2 52 8 12 25