❚❘×❮◆● ✣❸■ ❍➴❈ ❙× P❍❸▼ ❑ß ❚❍❯❾❚
✣➋ ❚❍■ ❈❯➮■ ❑Ý ❍➴❈ ❑Ý ■■ ◆❿▼ ❍➴❈ ✷✵✶✾ ✕ ✷✵✷✵
❚❍⑨◆❍ P❍➮ ❍➬ ❈❍➑ ▼■◆❍
▼æ♥✿ ❚♦→♥ ❝❛♦ ❝➜♣ ❆✷
❑❍❖❆ ❑❍❖❆ ❍➴❈ Ù◆● ❉Ö◆●
▼➣ ♠æ♥ ❤å❝✿ ▼❆❚❍✶✸✵✷✵✶
❇❐ ▼➷◆ ❚❖⑩◆
✣➲ sè✴▼➣ ✤➲✿ ✵✶ ✣➲ t❤✐ ❝â ✵✷ tr❛♥❣✳
✖✖✖✖✖✖✖✲ ❚❤í✐ ❣✐❛♥✿ ✾✵ ♣❤ót✳
✣÷ñ❝ ♣❤➨♣ sû ❞ö♥❣ t➔✐ ❧✐➺✉✳
❈➙✉ ■✿
✭✷ ✤✐➸♠✮ ●✐↔✐ ❤➺ ♣❤÷ì♥❣ tr➻♥❤ s❛✉
x1+ 2x2−4x3−4x4= 5
2x1+ 4x2= 2
2x1+ 3x2+ 2x3+x4= 5
−x1+x2+x3+ 6x4=−9
.
❈➙✉ ■■✿
✭✷ ✤✐➸♠✮ ❚r♦♥❣ ❦❤æ♥❣ ❣✐❛♥ ✈❡❝t♦r
R3
❝❤♦ ❤➺ ✈❡❝tì
(U)
❣ç♠ ❝→❝ ✈❡❝tì
u1= (1,−2,3), u2= (0,1,−3), u3= (1, m, −3).
❍➣② ①→❝ ✤à♥❤
m
✤➸ ❤➺
(U)
♣❤ö t❤✉ë❝ t✉②➳♥ t➼♥❤✳
❈➙✉ ■■■✿
✭✸ ✤✐➸♠✮ ❈❤♦ ♠❛ tr➟♥
B= 546
456
−4−4−5!.
✶✳✮ ❍➣② ❝❤➨♦ ❤â❛ ♠❛ tr➟♥ ❇✳
✷✳✮ ●✐↔ sû ♠❛ tr➟♥ ❝❤➨♦ ❤â❛ ✈ø❛ t➻♠ ✤÷ñ❝ ❧➔
C
✳ ❍➣② t➻♠ ♠❛ tr➟♥
T
✤➸
C=T−1BT
✳
❈➙✉ ■❱✿
✭✶ ✤✐➸♠✮ ❈❤♦ ❤➔♠ sè ➞♥
y=y(x)
✤÷ñ❝ ①→❝ ✤à♥❤ ❜ð✐ ♣❤÷ì♥❣ tr➻♥❤
ln px2+y2=a.arctg y
x.
❚➼♥❤
y′, y′′
✳
❈➙✉ ❱✿
✭✷ ✤✐➸♠✮ ❚➻♠ ❝ü❝ trà ❝õ❛ ❤➔♠ sè
z=x3+y3−3xy .
●❤✐ ❝❤ó✿ ❈→♥ ❜ë ❝♦✐ t❤✐ ❦❤æ♥❣ ✤÷ñ❝ ❣✐↔✐ t❤➼❝❤ ✤➲ t❤✐✳
❙è ❤✐➺✉✿ ❇▼✶✴◗❚✲P✣❇❈▲✲❘✣❚❱ ❚r❛♥❣ ✶
❈❤✉➞♥ ✤➛✉ r❛ ❝õ❛ ❤å❝ ♣❤➛♥ ✭❦✐➳♥ t❤ù❝✮ ◆ë✐ ❞✉♥❣
❦✐➸♠ tr❛
❬❈✣❘ ✽✳✽❪✿ ◆➢♠ ✈ú♥❣ ❝→❝ ❦❤→✐ ♥✐➺♠ ✈➲ ❤➺ ♣❤÷ì♥❣ tr➻♥❤ t✉②➳♥ t➼♥❤✳
❬❈✣❘ ✽✳✾❪✿ ⑩♣ ❞ö♥❣ ❝→❝ ♣❤÷ì♥❣ ♣❤→♣ ❣✐↔✐ ❤➺ ♣❤÷ì♥❣ tr➻♥❤ t✉②➳♥ t➼♥❤
✤➣ ✤÷ñ❝ ❤å❝✳
❈➙✉ ■
❬❈✣❘ ✽✳✸❪✿ ❇✐➳t ❝→❝❤ t➼♥❤ ✤à♥❤ t❤ù❝
❬❈✣❘ ✽✳✶✷❪✿ ❍✐➸✉ ✈➔ ✈➟♥ ❞ö♥❣ ❝→❝ ❦❤→✐ ♥✐➺♠ ❝õ❛ ❦❤æ♥❣ ❣✐❛♥ ✈➨❝tì✳ ❈➙✉ ■■
❬❈✣❘ ✽✳✶✼❪✿ ❚➻♠ ✤÷ñ❝ ❣✐→ trà r✐➯♥❣ ✈➔ ✈❡❝t♦r r✐➯♥❣ ❝õ❛ ♠❛ tr➟♥✳ ❳→❝
✤à♥❤ ✤÷ñ❝ ❦❤æ♥❣ ❣✐❛♥ ❝♦♥ r✐➯♥❣ t÷ì♥❣ ù♥❣ ✈î✐ ❝→❝ ❣✐→ trà r✐➯♥❣✳
❬❈✣❘ ✽✳✶✽❪✿ ◆➢♠ ✈ú♥❣ t❤✉➟t t♦→♥ ❝❤➨♦ ❤â❛ ♠❛ tr➟♥✳
❈➙✉ ■■■
❬❈✣❘ ✽✳✷✻❪✿ ❚➼♥❤ ✤÷ñ❝ ❝→❝ ✤↕♦ ❤➔♠ r✐➯♥❣ ❝➜♣ ♠ët ✈➔ ❝➜♣ ❝❛♦ ❝õ❛ ❤➔♠
♥❤✐➲✉ ❜✐➳♥✳
❬❈✣❘ ✽✳✷✼❪✿ ❚➻♠ ✤÷ñ❝ ❝ü❝ trà ❝õ❛ ❤➔♠ ♥❤✐➲✉ ❜✐➳♥✳
❈➙✉ ■❱
◆❣➔② ✶✹ t❤→♥❣ ✵✼ ♥➠♠ ✷✵✷✵
❚❤æ♥❣ q✉❛ ❚r÷ð♥❣ ❜ë ♠æ♥
✭❦þ ✈➔ ❣❤✐ rã ❤å t➯♥✮
❙è ❤✐➺✉✿ ❇▼✶✴◗❚✲P✣❇❈▲✲❘✣❚❱ ❚r❛♥❣ ✷