Sc ie nc e an d ed ucat I o m

0 1 2 _

4 3 0 ^

 

, ,e e e

^ 2 1 2 ^

7. 
   misol. ^{1 2 3}
   

bazisda chiziqli operatorning matritsasi ^{ }

^{ '}  2  2  2e e e e
1 1 2 3


e^'

e e e

 e^'  e e e

koʻrinishda. Yangi ^
3 1 2 3
bazisda ^A operatorning matritsasini toping.

7. 
   misol.
   

tekshiring.
^A_^x_ ^ ^{2x1 x3;4x2}
2x₃; 3x₁ x₂
^x3 


operatorni chiziqlilikka

Yechish. Operatorni chiziqlilikka tekshirish uchun
A_x y_
A_x_
A_y_ 

hamda
A_ x_   A_x_

tengliklarni bajarilishini tekshirish kifoya.

 2_ x₁  y_{1 }  x₃  y₃
^ _ 2x₁  x₃  2 y₁  y_{3 }

^A_^{x  y} _ ^{  4} ^{x y}  ² ^{x y}  ^{  4x 2x 4 y 2 y }
_ ^{2 2 3 3} _{ } 2 3 2 3 _
^{ 3} ^{x1  y1}  ^{ x2 y2}  ^{x3 y3} ^{ } 3x₁ x₂ x₃3y₁ y₂ y₃ ^
  ^{ }

2x₁ — x₃ 2y + y₃
= 4x₂ — 2x + 4J₂ — 2y₃ = A x) y)
^{3x x}2 ^{— x}3 ³y + r2— y3
2m_{=1+ 3} 2x + x₃
A a:x) —— 4œx₂ — 2œx₃ = œ 4x₂ — 2x₃ = a >)
^{3axț +} 2 ^Ñ3 ^3*i + *z *s
A —— ^{1 4}

7. 
   TYllSOl Chizqli operator ^{9 1} matritsa bilan berilgan. Chiziqli operatorning hos qiymatlari va hos vektorlarini toping.
   

Yechish. Xarakteristik tenglama tuzamiz: 2² — 22 —35 = 0, = —5, = 7
1 — 1 4
9 1— I ⁼⁰

1
^{' 5} X^{os qiymatga mos ‘ ’' ( 1 )} X^{os vektorni topamiz. Buning uchun} quyidagi tenglamani yechamiz:
= —5, p A — BE) - x —— 8, = —1,5x

1
Agar ^{' C} deb olsak, *^{2' 1 5C} bo‘ladi. Demak ‘’ ’ ^{(c; — 1.5c)} Vector ^A

operatorning ^{' 5} xos qiymatiga mos xos vector bo‘ladi. Xuddi shunga o‘xshab
(2) 2
^{' 7} xos qiymatga mos xos vektorlarni ³ aniqlash mumkin.


Foydalanilgan adabiyotlar

1. 
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2. 
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4. 
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5. 
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1995.

6. 
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2017.

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