(^220) Solutions
$•
00
0i
1
= (A<A)-Wy=^
11
-3
11111
12345
0 =
0o
0i
= {A^1 A)^A*y
10
" 11 -3'
-3 1
"20"
72 =
'0.4'
1.2 =
'0o
01
5 = 3, y = 4,
SSxy = (l-3)(l-4)+(2-3)(4-4)+(3-3)(4-4)+(4-3)(4-4)+(5-3)(7-4) = 12,
SSXX = (1 - 3)^2 + (2 - 3)^2 + (3 - 3)^2 + (4 - 3)^2 + (5 - 3)^2 = 10.
12 -
ft = -,#> = 4-1.2(3) = 0.4.
3.3
(a) Let us interchange the first two equations to get A[ = LU:
A[ =
Here, the form of L is a bit different, but serves for the purpose. We solve
LUx = 6'j = [19,8,3]T in two stages: Lc = b', then Ux = c.
"2 1 3"
1 32
32 1

• 2
  3
  1
  3
  1

"Ml

1 0

0 0

"3 2 1"

(^0) u Ii
3 3
0 Of _
Lc =b[ & §
Ux = c<=>
Final check:

• 2
  3
  1
  3
  1

-Ml

10

0 0_

"ci"

C2

.C3.

__

'19"

8

3

=*• c 3 = 18.

<^> c^2 = 7

ci = 3

3 2 1

nil U

3 3

0 0 f _

'xi

X2

.X3.

_

" 3"

7

_18_

=> xi = 0.

<£> => x 2 = -2

x 3 = 7

Aix =

"132"

2 1 3

32 1_

0'

-2

7

=

" 8"

19

3_

/