Question

find the matrix X such that AX=B , where A=[1/2 -1/2] and B=[0/1 2/4]​

Answer 1

Step-by-step explanation:

Given that :

$A=\left[\begin{array}{cc}1&-1\\2&2\end{array}\right]\\\\B=\left[\begin{array}{cc}0&2\\1&4\end{array}\right]$

To find: find the matrix X such that AX=B

Solution: To find X,First of all we have to find inverse of A.

$AX=B \\ X = {A}^{ - 1} \times B \\ \\ X = \frac{adj(A)}{ |A| } \times B$

$adj(A)=\left[\begin{array}{cc}2&1\\-2&1\end{array}\right]\\\\and\:|A|=2+2=4\\\\X=\frac{1}{4}\left[\begin{array}{cc}2&1\\-2&1\end{array}\right]\times\left[\begin{array}{cc}0&2\\1&4\end{array}\right]$

$X=\frac{1}{4}\left[\begin{array}{cc}0+1&4+4\\0+1&-4+4\end{array}\right]\\\\=\frac{1}{4}\left[\begin{array}{cc}1&8\\1&0\end{array}\right]$

$X=\frac{1}{4}\left[\begin{array}{cc}1&8\\1&0\end{array}\right]$

$X=\left[\begin{array}{cc}\frac{1}{4}&\frac{8}{4}\\\\\frac{1}{4}&\frac{0}{4}\end{array}\right]$

$X=\left[\begin{array}{cc}\frac{1}{4}&2\\\\\frac{1}{4}&0\end{array}\right]$

Hope it helps you.