Question

macierze:

A*xB

x*[1 0 1 = [0 1 -2

2-1 0 2 -1 0]

3 2 1]

Answer 1

Czy: 

     [0 1 -2]

A=

     [2 -1 0]

--------

    [1  0 1]

B=[2 -1 0]

    [3  2 1]

Jeśli taj jest, to:

XB=A

Macierz X:

    [a b c]

X=

    [d e f]

--------------

[a b c] [1  0 1]  [0 1 -2]

           [2 -1 0]= 

[d e f] [3  2 1]  [2 -1 0]

Należy rozwiązać dwa układ równań:

1. 

{a+2b+3c=0

{-b+2c=1

{a+c=-2

---

{-2-2+4c+2c=0

{-1+2c=b

{a=-2-c

---

{c=2/3

{b=1/3

{a=-8/3

------------

2.

{d+2e+3f=2

{-e+2f=-1

{d+f=0

---

{e=1-f

{-1+f+2f=-1

{d=-f

---

{e=1

{f=0

{d=0

=======================

Czyli macierz X to:

[-8/3  1/3  2/3]

[   0     1      0  ]