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MAA MATHEMATICAL ASSOCIATION OF AMERICA K webwork / s118anikakhtm2360sd01 / hw2 29 HW2: Problem 29 Previous Problem ListNext (1 point) Find the LU factorization of A=| 12-14-71. -8 8-3 A-"LUwhere Lis a lower triangular matrix with ones onthe diagonal, and U is an upper triangular matrix Note: You can eam partial credit on this probiem Preview My Answers Subemit Answers You have attempted this problem 0 imes You have unlienited atenmpts remaining

Answer 1

29. Let U =

a	b	c
0	d	e
0	0	f

Also, let L =

1	0	0
p	1	0
q	r	1

Then LU =

a+bp+cq	b+cr	c
dp+eq	d+er	e
fq	fr	f

Now, since A = LU, we have c = 3, e = -7, f = -3,

fr = 8 so that r = 8/f = -8/3, b+cr = 5 or, b+3*(-8/3)= 5 or, b-8 = 5 so that b =5+8 = 13, d+er = -14 or,            d +(-7)*(-8/3) = -14 or, d+56/3 = -14 so that d = -13-56/3 = -98/3,

fq = -8 or, -3q = -8 so that q = 8/3, dp+aq = 12 or, (-98/3)p+(-7)*(8/3) = 12 or,-98p/3 -56/3 = 12 or,                         -(98p+56)/3 = 12 or, 98p+56 = -36 or, 98p = -36-56 = 92 so that p = -92/98 = -46/49 and a+bp+cq = -4 or, a +13*(-46/49)+3*(8/3) = -4 or, a-598/49 +8 = -4 so that a = -4-8 +598/49 = 10/49.

Thus, U =

10/49	13	3
0	-98/3	-7
0	0	-3

and L =

1	0	0
-46/49	1	0
8/3	-8/3	1