Question

REZOLVATI SISTEMELE MATRICE
 X+2Y= 1    2
             3   4
X-2Y=  1    3
            5    7 

2X-3Y= -1    2
               3    4

3X-2Y=  1   -1
               2    3
              

Answer 1

A) $X+2Y= \left[\begin{array}{ccc}1&2\\3&4\\\end{array}\right]$
$X-2Y= \left[\begin{array}{ccc}1&3\\5&7&\\\end{array}\right]$
2Y, -2Y se reduc asa ca avem: $2X= \left[\begin{array}{ccc}1&2&\\3&4\\\end{array}\right] + \left[\begin{array}{ccc}1&3\\5&7\\\end{array}\right]$
$2X= \left[\begin{array}{ccc}2&5\\8&11\\\end{array}\right]$
$X= \left[\begin{array}{ccc}1& \frac{5}{2} \\4& \frac{11}{2} \\\end{array}\right]$
Apoi inlocuim in prima sau a doua ecuatie pentru a-l afla pe Y, eu zic in prima:
$2Y= \left[\begin{array}{ccc}1&2\\3&4\\\end{array}\right] - \left[\begin{array}{ccc}1& \frac{5}{2} \\4& \frac{11}{2} \\\end{array}\right]$
[tex] 2Y= \left[\begin{array}{ccc}0& \\ \frac{-1}{2} \\ -1&\frac{-3}{2} \\\end{array}\right] [/tex]
$Y= \left[\begin{array}{ccc}0& -1\\ \frac{-1}{2} &-3\\\end{array}\right]$