# Matrix

• Nov 23rd 2012, 04:44 AM
Petrus
Matrix
Hello i got a problem!
ima decide a inverkar to this Matrix A=1 0 -1 1 an it says clue ima set B= x y z tand decide x,y,z,t, for B shall be inverse to A.( its 2x2 the first 2 number are the number on top and the last 2 is at bottom idk what u say on english

Its a 2x2 Matrix sorry for not writing it with latex and sorry for My bad english.
So i did A•B and get C= 1x 1y, -1x+z, -1y+1t
idk why i did not write as t insted of having one before byt hope u guys did understand and looking forward to se all help
• Nov 23rd 2012, 09:00 AM
chiro
Re: Matrix
Hey Petrus.

Do you just want to find the inverted matrix of A given what is written in the attachment?

If the answer is yes, here is the Octave output for this problem:

>> A = [1, 0; -1, 1]
A =

1 0
-1 1

>> inv(A)
ans =

1 0
1 1
• Nov 23rd 2012, 09:09 AM
Deveno
Re: Matrix
suppose we want to invert:

$A = \begin{bmatrix}1&0\\-1&1 \end{bmatrix}$

$B = \begin{bmatrix}x&y\\z&t \end{bmatrix}$.

so we calculate:

$AB = \begin{bmatrix} x&y\\z-x&t-y \end{bmatrix}$

if B is to be the inverse of A, we must have AB = I.

thus:

x = 1
y = 0
z - x = 0
t - y = 1

from z - 1 = 0, we get z = 1.
from t - 0 = 1, we get t = 1.

thus:

$A^{-1} = B = \begin{bmatrix}1&0\\1&1 \end{bmatrix}$