Determinantarvutus
Determinandid, lineaarsed võrrandisüsteemid
Ülesanne 1
Lahenda võrrandisüsteem determinantide abil.
x + y + z = 26
3x - y + z = 20
- x + 7 y - 2 z = 15
1 1 1 1 1
D = 3 - 1 1 3 - 1 = 2 - 1 + 21 - 1 - 7 + 6 = 20
-1 7 - 2 -1 7
26 1 1 26 1
Dx = 20 - 1 1 20 - 1 = 52 + 15 + 140 + 15 - 182 + 40 = 80
15 7 - 2 15 7
1 26 1 1 26
Dy = 3 20 1 3 20 = - 40 - 26 + 45 + 20 - 15 + 156 = 140
- 1 15 - 2 - 1 15
1 1 26 1 1
Dz = 3 - 1 20 3 - 1 = - 15 - 20 + 546 - 26 - 140 - 45 = 300
- 1 7 15 - 1 7
Dx 80
x = D = 20 = 4
Dy 140
y= = = 7
D 20
Dz 300
z = D = 20 = 15
Kontroll:
I
vp1 = 4 + 7 + 15 = 26
pp1 = 26
vp1 = pp1
II
vp 2 = 3 4 - 7 + 15 = 20
pp 2 = 20
vp 2 = pp 2
III
vp 3 = -4 + 7 7 - 2 15 = 15
pp 3 = 15
vp 3 = pp 3
x= 4
Vastus: y = 7
z = 15
Ülesanne 2
Lahend...
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