Four by Four.xlsx

	B	C	D	E	F	G	H	I	J	K	L	M	O	P	Q	R
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3		Solving 4 linear equations in 4 unknowns
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5		A a 4x4 non-singular matrix
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7		b a 4x1 column vector
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9		Perform a Gram Schmidt procedure of the columns of A
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58		Input
59
60		Columns of A							Columns of Q
61
62		A1	A2	A3	A4		b		C1	C2	C3	C4
63	1	2.5	-5.2	11.3	-4.2		1.3		0.3542981997	-0.3553553378	0.8302626103	0.242609496	1
64	2	3.2	8.1	-4.3	6.1		-3.8		0.4535016956	0.7827375194	0.2436731558	-0.3496878336	1	0.00000000
65	3	5.1	-7.3	3.1	-2.6		-52.6		0.7227683274	-0.4474814425	-0.399763106	-0.3428640586	1	0.00000000	0.00000000
66	4	2.7	1.9	-3.8	15.2		-48.5		0.3826420557	0.2465865331	-0.3024514014	0.8374385284	1	0.00000000	0.00000000	0.00000000
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68							Orthonormal Checks		1	1	1	1	Col1	Col2	Col3	Col4
69										0.00000000	0.00000000	0.00000000	2.5	-4.236955212	6.844869794	2.539746959
70											0.00000000	0.00000000	3.2	9.332697329	2.008895744	-3.66069188
71												0.00000000	5.1	-5.335388632	-3.295736042	-3.589257488
72													2.7	2.940088371	-2.493476685	8.766688818
73		Solution				b - sum(xn-jAn-j,j,0,k-1)							7.056202945	11.92315061	8.244222623	10.46845651
74						k
75		x4 =	-2			1	2	3
76		x3 =	3			-7.1	-41	-15
77		x2 =	5			8.4	21.3	-19.2
78		x1 =	-6			-57.8	-67.1	-30.6
79						-18.1	-6.7	-16.2
80
81		Splution Check
82		Input
83		b			A			x
84		1.3		2.5	-5.2	11.3	-4.2	-6		1.3
85		-3.8		3.2	8.1	-4.3	6.1	5	=	-3.8
86		-52.6		5.1	-7.3	3.1	-2.6	3		-52.6
87		-48.5		2.7	1.9	-3.8	15.2	-2		-48.5
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